Low contrast anti-reflection articles with reduced scratch and fingerprint visibility

ABSTRACT

Embodiments of articles including a low-contrast anti-reflection coating are disclosed. The coated surface of such articles exhibits a reduced difference in reflectance between a pristine state and when a surface defect is present. In one or more embodiments, the coated surface of such articles exhibits a first average reflectance in the range from about 0.6% to about 6.0% in a pristine condition and a second average reflectance of about 8% or less after removal of a surface thickness of the anti-reflection coating. In other embodiments, the coated substrate exhibits a second average reflectance of about 10% or less, when the coated surface comprises a contaminant. In some embodiments, the coated substrate exhibits a first color coordinate (a* 1 , b* 1 ) in a pristine condition and a second color coordinate (a* 2 , b* 2 ) after the presence of a surface defect such that Δa*b* is about 6 or less.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a Continuation of U.S. application Ser. No.15/313,733, filed on Nov. 23, 2016, which claims the benefit of priorityunder 35 U.S.C. § 371 of International Patent Application Serial No.PCT/US15/32138, filed on May 22, 2015, which in turn, claims the benefitof priority of U.S. Provisional Patent Application Ser. No. 62/002,466filed on May 23, 2014, the contents of each of which are relied upon andincorporated herein by reference in their entireties.

BACKGROUND

The disclosure relates to articles with a low contrast, anti-reflectioncoating and more particularly to such articles with reduced surfacedefect (e.g., scratches and fingerprints) visibility.

Transparent, scratch resistant films and hard coatings are used in thedisplay cover glass market and other applications such as architectural,automotive, or other applications requiring high optical transmissionand surface durability. These films and coatings have also been shown toimprove the resistance to damage, during drop events onto hard and roughsurfaces.

Anti-reflection coatings have also been developed for these markets andapplications to reduce the intensity of reflected ambient light from asurface, to increase the transmittance, the readability and viewabilityof displays, and to reduce unwanted or distracting glare fromeyeglasses, windows and other surfaces. Conventional anti-reflectioncoatings suffer from drawbacks including an increased visibility ofsurface defects (as described herein) when compared to surfaces with thesame surface defects but that do not include an anti-reflection coating.As shown in FIG. 1, the visibility of a surface defect depends at leastin part on reflectance contrast between a pristine portion of ananti-reflection coating and surface defect-containing portion of thesame anti-reflection coating. FIG. 1 illustrates a known article 10 witha substrate 20 with a surface 22, and anti-reflection coating 30disposed on the surface 22 forming a coated surface 32. In FIG. 1, theremoval of a portion of the anti-reflection coating 30 (i.e., formationof a surface defect on the coated surface 32) forms a new surface thatincludes a surface defect 34. The coated surface 32 that is free ofsurface defects is considered pristine. As used herein, the phrase“pristine” means a coated surface that is free of surface defects, asdefined herein. As shown in FIG. 1A, the pristine coated surface has afirst reflectance % R₁ and the surface including a surface defect (shownby the removal of a surface thickness) exhibits a second reflectance %R₂ that is different from % R₁. Some anti-reflection coatings includealternating high refractive index layers and low refractive indexlayers, the second reflectance % R₂ differs from % R₁ because thematerial at the exposed surface that includes the surface defect 34 isdifferent from the material at the pristine surface. This result is alsopresent when the surface defect includes the addition of a contaminanton the coated surface, instead of the removal of a surface thickness.This difference in reflectance highlights the presence of a surfacedefect, which may be enhanced by the presence of a surface defect havingvarying surface thicknesses removed thickness, depending on thestructure of the anti-reflection coating.

In addition, recently emerging coating materials for display covers mayhave high hardness or other improved mechanical properties; however,these improved mechanical properties are often fundamentally associatedwith materials having a higher refractive index, such as Al₂O₃,single-crystal Al₂O₃ (sapphire), AlNx, AlOxNy, SiNx, SiOxNy, and ZrO₂.

Accordingly, there is a need for specially designed coatings that reducethe reflectance associated with articles with high-index materialsand/or transparent substrates, without substantially increasing thevisibility of surface defects that may appear or form during use of thearticles. The present disclosure relates to reduce reflectance, ascompared to the same bare transparent substrates, while reducingvisibility of surface defects.

SUMMARY

Various aspects of this disclosure related to transparent articlesexhibiting low reflectance and reduced visibility of surface defects.The articles include an anti-reflection coating disposed on at least onesurface that reduces the reflectance of the article and has attributesthat reduce the contrast or visibility of surface defects. As usedherein, the phrase “surface defects” includes the removal of a surfacethickness of the anti-reflection coating (e.g., scratches, chips, and/orabraded areas on or in the anti-reflection coating); the addition of amaterial or contaminant to the coated surface of the anti-reflectioncoating (e.g., fingerprints, fingerprint residue(s) orfingerprint-simulating medium or media); delaminated areas of theanti-reflection coating; and other surface flaws that are introduced inand/or to the anti-reflective coating during normal use of the articles(i.e., not introduced during manufacture of the article or dispositionof the anti-reflective coating). Surface defects should have a lateraldimension of about 1 μm or greater.

A first aspect of this disclosure pertains to articles including asubstrate with a substrate surface, and an anti-reflection coatingdisposed on the substrate surface forming a coated surface. Unlessotherwise specified, the coated surface is the surface of theanti-reflection coating and the underlying substrate (and/or otherlayers disposed between the substrate and the anti-reflection coating).In one or more embodiments, the coated surface exhibits a first averagereflectance in the range from about 0.6% to about 6.0% over at least aportion of the visible spectrum in the range from about 450 to about 650nm, when the coated surface is in a pristine condition, and a secondaverage reflectance of about 8% or less (e.g., about 3% or less) overthe visible spectrum, after removal of a surface thickness of theanti-reflection coating from the coated surface. In one variant, theanti-reflection coating comprises a coating thickness that is greaterthan the surface thickness. In another variant, the surface thickness isabout 25 nm or greater (e.g., in the range from about 25 nm to about 100nm or from about 25 nm to about 500 nm). In yet another variant, theanti-reflection coating includes multiple layers and specificallyincludes a first layer disposed on the substrate surface and a secondlayer disposed on the first layer, wherein the second layer has a havinga thickness that is less than the surface thickness (or in other words,the surface thickness is greater than or equal to the layer thickness ofthe second layer).

In one embodiment, the coated surface may exhibit a first reflectancewhen the coated surface is in a pristine condition, and a secondreflectance after removal of a surface thickness of the anti-reflectioncoating from the coated surface. At least one of the first reflectanceand the second reflectance may exhibit an average oscillation amplitudeof about 2% absolute reflectance or less, over the visible spectrum. Insome embodiments, at wavelength widths of about 100 nm within thevisible spectrum, at least one of the first reflectance and the secondreflectance exhibits a maximum oscillation amplitude of about 2%absolute reflectance or less. The reflectances of such embodiments maybe measured under an incident illumination angle in the range from about0 degrees to about 60 degrees. In some embodiments, at least one of thefirst reflectance and the second reflectance comprises reflectanceoscillations of less than 20% relative to a mean reflectance value, overthe visible spectrum.

In one or more embodiments, the coated surface comprises a contrastratio (the second average reflectance:the first average reflectance) inthe range from about 0.5 to about 50, over the visible spectrum. In oneor more embodiments, wherein the surface thickness comprises up to about25 nm, the second average reflectance comprises about 6% or less, andthe coated surface exhibits a contrast ratio (the second averagereflectance:the first average reflectance) in the range from about 0.5to about 10, over the visible spectrum. In some embodiments, wherein thesurface thickness comprises up to about 50 nm, the second averagereflectance comprises about 8% or less, and the coated surface exhibitsa contrast ratio (the second average reflectance:the first averagereflectance) in the range from about 0.5 to about 20, over the visiblespectrum. In some embodiments, wherein the surface thickness comprisesup to about 500 nm, the second average reflectance comprises about 12%or less, and the coated surface exhibits a contrast ratio (the secondaverage reflectance:the first average reflectance) in the range fromabout 0.5 to about 50, over the visible spectrum. In one or moreembodiments, the coated surface exhibits a contrast ratio of (the secondaverage reflectance:the first average reflectance) of about less than10, over the visible spectrum, and the first average reflectance and thesecond average reflectance are measured under an incident illuminationangle in the range from about 0 degrees to about 60 degrees. Thecontrast ratio exhibited by some embodiments may exhibit oscillationshaving an average amplitude of about 1 or less in absolute ratio units,over the visible spectrum. In other embodiments, the first averagereflectance and the second average reflectance are measured under anincident illumination angle in the range from about 0 degrees to about60 degrees.

A second aspect of this disclosure pertains to an article including asubstrate having a surface, and an anti-reflection coating disposed onthe surface forming a coated surface in which the coated surfaceexhibits a first average reflectance when the anti-reflection coating isimmersed in air and a second average reflectance that is about equal toor less than the first average reflectance (and may be less than about1%) when the anti-reflection coating is immersed in afingerprint-simulating medium. The fingerprint-simulating medium caninclude a refractive index in the range from about 1.4 to about 1.6.

A third aspect of this disclosure includes an article with a substratehaving a surface, and an anti-reflection coating disposed on the surfaceforming a coated surface, in which the coated surface of the articleexhibits a first average reflectance in the range from about 0.6% toabout 6.0% over a visible spectrum in the range from about 450 to about650 nm when the article is in a pristine condition, and a second averagereflectance of about 10% or less over the visible spectrum, when thecoated surface comprises a layer of fingerprint-simulating medium. Thelayer of fingerprint simulating medium may have a thickness in the rangefrom about 100 nm to about 2000 nm, and an include a refractive index of1.4-1.6.

The contrast ratio of the second average reflectance to the firstaverage reflectance is about 20 or less, and the ratio comprisesoscillations having an average amplitude of about 10 or less in absoluteratio units, over the visible spectrum. In some embodiments, the coatedsurface comprises the layer of fingerprint-simulating medium and amaximum reflectance value of about 8% absolute reflectance or less,across the visible spectrum, and the coated surface comprises the layerof fingerprint-simulating medium and a reflectance comprising a maximumoscillation amplitude of about 7.5% absolute reflectance or less, acrossthe visible spectrum.

A fourth aspect of this disclosure pertains to an article including asubstrate surface and an anti-reflection coating disposed on thesubstrate surface forming a coated surface, wherein the coated surfaceexhibits a first color coordinate (a*₁, b*₁), when measured using anincident illumination angle in the range from about 0 degrees to about75 degrees from normal incidence under an illuminant in a pristinecondition, and a second color coordinate (a*₂, b*₂), when measured usingthe incident illumination angle under the illuminant after removal of asurface thickness of the anti-reflection coating from the coatedsurface. The incident illumination angle may be about 60 degrees, andthe surface thickness may be in a range from about 0.1 to about 100 nm.

The difference in color coordinates (Δa*b*) may be about 6 or less oreven about 3 or less. In some embodiments the surface thickness is inthe range from about 0.1 nm to about 140 nm. The anti-reflection coatingmay have a first layer disposed on the surface and a second layerdisposed on the first layer, wherein the first layer comprises ahigh-index material layer having a thickness of about 50 nm or less. Inanother embodiment, the anti-reflection coating includes a hard materialhaving a hardness of greater than about 5 GPa, as measured by aBerkovich Indenter Hardness Test, as defined herein, over an indentationdepth of about 100 nm or greater. In some embodiments, the articleexhibits a hardness of about 5 GPa or greater as measured by a BerkovichIndenter Hardness Test, as defined herein, over an indentation depth ofabout 100 nm or greater.

Additional features and advantages will be set forth in the detaileddescription which follows, and in part will be readily apparent to thoseskilled in the art from that description or recognized by practicing theembodiments as described herein, including the detailed descriptionwhich follows, the claims, as well as the appended drawings.

It is to be understood that both the foregoing general description andthe following detailed description are merely exemplary, and areintended to provide an overview or framework to understanding the natureand character of the claims. The accompanying drawings are included toprovide a further understanding, and are incorporated in and constitutea part of this specification. The drawings illustrate one or moreembodiment(s), and together with the description serve to explainprinciples and operation of the various embodiments.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a side view of a known article including a substrate and ananti-reflection coating;

FIG. 2 is a side view of an article according to one or more embodimentswith a surface defect that includes the removal of a surface thickness;

FIG. 3 is a side view of an article according to one or more embodimentswith a multi-layered anti-reflection coating and a surface defect thatincludes the removal of a surface thickness;

FIG. 4 is a side view of an article according to one or more embodimentswith a surface defect that includes the addition of a contaminant;

FIG. 5A is graph of reflectance spectra of the article of ModeledComparative Example 1, after removal of different surface thicknesses;

FIG. 5B is a graph showing the contrast ratio of the article shown inFIG. 5A, after removal of different surface thicknesses;

FIG. 5C is a graph showing the contrast ratio of Modeled ComparativeExample 2, after removal of different surface thicknesses;

FIG. 5D is a graph showing Δa*b* of the article shown in FIG. 5A, as afunction of surface thickness removal and incident illumination angle;

FIG. 6A is a graph of reflectance spectra of Modeled Example 3, afterremoval of different surface thicknesses;

FIG. 6B is a graph showing the contrast ratio of the article shown inFIG. 6A, after removal of different surface thicknesses;

FIG. 6C is a graph showing Δa*b* of the article shown in FIG. 6A, as afunction of surface thickness removal and incident illumination angle;

FIG. 7A is a graph of reflectance spectra of Modeled Example 4, afterremoval of different surface thicknesses;

FIG. 7B is a graph showing the contrast ratio of the article shown inFIG. 7A, after removal of different surface thicknesses;

FIG. 7C is a graph of reflectance spectra of Modeled Example 4 in thepristine condition at different incident viewing angles;

FIG. 7D is a graph showing Δa*b* of the article shown in FIG. 7A, as afunction of surface thickness removal and incident illumination angle;

FIG. 8A is a graph of reflectance spectra of Modeled Example 5, afterremoval of different surface thicknesses;

FIG. 8B is a graph showing the contrast ratio of the article shown inFIG. 8A, after removal of different surface thicknesses;

FIG. 8C is a graph of reflectance spectra of Modeled Example 5 in thepristine condition at different incident viewing angles;

FIG. 8D is a graph showing Δa*b* of the article shown in FIG. 8A, as afunction of surface thickness removal and incident illumination angle;

FIG. 9A is a graph of reflectance spectra of Modeled Example 6, afterremoval of different surface thicknesses;

FIG. 9B is a graph showing the contrast ratio of the article shown inFIG. 9A, after removal of different surface thicknesses;

FIG. 9C is a graph of reflectance spectra of Modeled Example 6 in apristine condition, at different incident illumination angles;

FIG. 9D is a graph showing the change in reflectance of Modeled Example6, after removal of 50 nm of surface thickness, at different incidentillumination angles;

FIG. 9E is a graph showing the contrast ratio of the coated surfaceshown in FIG. 9D;

FIG. 9F is a graph showing Δa*b* of the article shown in FIG. 9A, as afunction of surface thickness removal and incident illumination angle;

FIG. 10A is a graph of reflectance spectra of Comparative ModeledExample 7 with a surface defect that includes the addition of acontaminant having different thicknesses;

FIG. 10B is a graph showing the contrast ratio of the article shown inFIG. 10A, after the addition of a contaminant having differentthicknesses;

FIG. 11A is a graph of reflectance spectra of Modeled Example 8 with asurface defect that includes the addition of a contaminant havingdifferent thicknesses;

FIG. 11B is a graph showing the contrast ratio of the article shown inFIG. 11A, after the addition of a contaminant having differentthicknesses;

FIG. 12A is a graph of reflectance spectra of Modeled Example 9 with asurface defect that includes the addition of a contaminant havingdifferent thicknesses;

FIG. 12B is a graph showing the contrast ratio of the article shown inFIG. 12A, after the addition of a contaminant having differentthicknesses;

FIG. 13A is a graph of reflectance spectra of Modeled Example 10 with asurface defect that includes the addition of a contaminant havingdifferent thicknesses;

FIG. 13B is a graph showing the contrast ratio of the article shown inFIG. 13A, after the addition of a contaminant having differentthicknesses;

FIG. 14A is a graph of reflectance spectra of Modeled Example 11 atdifferent incident illumination angles;

FIG. 14B is graph showing the a* and b* coordinates for Modeled Example11 at different incident illumination angles and under illuminants D65and F2;

FIG. 15A is a graph of reflectance spectra of Modeled Example 12 atdifferent incident illumination angles; and

FIG. 15B is graph showing the a* and b* coordinates for Modeled Example12 at different incident illumination angles and under illuminants D65and F2.

DETAILED DESCRIPTION

Reference will now be made in detail to various embodiment(s), examplesof which are illustrated in the accompanying drawings. Wheneverpossible, the same reference numerals will be used throughout thedrawings to refer to the same or like parts.

A first aspect of the present disclosure pertains to an articleincluding a low contrast, anti-reflection coating. As shown in FIG. 2,the article 100 includes a substrate 200 with at least one substratesurface 220 and an anti-reflection coating 300 disposed on the at leastone substrate surface, forming a coated surface 320, that reduces thereflectance of the article. In other words, the coated surface 320exhibits a low reflectance or a reflectance that is less than thereflectance of the substrate surface 220 without the anti-reflectioncoating 300 disposed thereon. As used herein, the term “reflectance” isdefined as the percentage of incident optical power within a givenwavelength range that is reflected from a material (e.g., the article,the substrate, or the optical film or portions thereof). Reflectance ismeasured using a specific linewidth. In one or more embodiments, thespectral resolution of the characterization of the reflectance is lessthan 5 nm or 0.02 eV.

The average reflectance (% R_(av1) and % R_(av2)) and the reflectance (%R₁ and % R₂) values and ranges described herein may be measured usingunder an incident illumination angle, which simulates the colorexhibited or perceived in reflection of the coated surface, as theviewing angle changes. The incident illumination angle may be in therange from about 0 degrees to about 80 degrees, from about 0 degrees toabout 75 degrees, from about 0 degrees to about 70 degrees, from about 0degrees to about 65 degrees, from about 0 degrees to about 60 degrees,from about 0 degrees to about 55 degrees, from about 0 degrees to about50 degrees, from about 0 degrees to about 45 degrees, from about 0degrees to about 40 degrees, from about 0 degrees to about 35 degrees,from about 0 degrees to about 30 degrees, from about 0 degrees to about25 degrees, from about 0 degrees to about 20 degrees, from about 0degrees to about 15 degrees, from about 5 degrees to about 80 degrees,from about 5 degrees to about 80 degrees, from about 5 degrees to about70 degrees, from about 5 degrees to about 65 degrees, from about 5degrees to about 60 degrees, from about 5 degrees to about 55 degrees,from about 5 degrees to about 50 degrees, from about 5 degrees to about45 degrees, from about 5 degrees to about 40 degrees, from about 5degrees to about 35 degrees, from about 5 degrees to about 30 degrees,from about 5 degrees to about 25 degrees, from about 5 degrees to about20 degrees, from about 5 degrees to about 15 degrees, and all ranges andsub-ranges therebetween. The illuminants used to measure averagereflectance (% R_(av1) and % R_(av2)) and the reflectance (% R₁ and %R₂) values and ranges described herein may include standard illuminantsas determined by the CIE, including an A illuminants (representingtungsten-filament lighting), B illuminants (daylight simulatingilluminants), C illuminants (daylight simulating illuminants), D seriesilluminants (representing natural daylight), and F series illuminants(representing various types of fluorescent lighting).

The anti-reflection coating 300 can be described as a “low-contrast”coating, as the contrast or visibility of surface defects in or on theanti-reflection coating is reduced, compared to a conventionalanti-reflection coating. Contrast and visibility may be described interms of relative reflectance between surfaces with and without surfacedefects.

Accordingly, the relative differences in the reflectance of theant-reflection coatings in pristine condition and the same coating witha condition including a surface defect can be used to describe the lowcontrast attribute of the anti-reflection coatings described herein.Specifically, the ratios of the reflectances (i.e., contrast ratio),reflectance oscillations vs. wavelength and oscillations in contrastratio vs. wavelength of the anti-reflection coating in a pristinecondition and in a condition with a surface defect each individually andcollectively influence the visibility and color of the anti-reflectioncoating and surface defects contained therein. Thus lower or smalleroscillations in reflectance and contrast ratios and smaller contrastratios contribute to lower visibility of surface defects. Such surfacedefects can often create light scattering due to the defect size andshape; the performance of the anti-reflection coating of one or moreembodiments generally neglects scattering effects, which is independentof the other optical behaviors described herein. Even in the presence oflight scattering from surface defects, the optical performance of theanti-reflection coating embodiments describe herein significantly reducethe visibility of surface defects.

In one or more embodiments, the coated surface 320 exhibits a firstaverage reflectance (% R_(av1)) or a first reflectance (% R₁) over atleast a portion of the visible spectrum when the coated surface is inpristine condition and a second average reflectance (% R_(av2)) or asecond reflectance (% R₂) over at least a portion of the visiblespectrum when the coated surface comprises a surface defect 340, asdescribed herein. The relative differences between % R₁ and % R₂, andbetween % R_(av1) and % R_(av2) is reduced when compared to knowncoatings. As used herein, the phrase “visible spectrum” includeswavelengths along the range from about 400 nm to about 700 nm or fromabout 450 nm to about 650 nm. The reflectance values or ranges describedherein may be qualified as being across the visible spectrum or along aportion of the visible spectrum. A portion of the visible spectrum maybe described as a “wavelength width”, which may be a width of about 100nm or 200 nm within the visible spectrum (e.g., from about 400 nm toabout 500 nm, or from about 450 nm to about 650 nm.

In one or more specific embodiments, the surface defect 340 comprisesthe removal of a surface thickness 360 of the anti-reflection coatingfrom the coated surface of about 25 nm or more, as shown in FIG. 2. Insome embodiments, the surface thickness may be in the range from about25 nm to about 500 nm. For example, the surface thickness may be in therange from about 25 nm to about 450 nm, from about 25 nm to about 400nm, from about 25 nm to about 350 nm, from about 25 nm to about 300 nm,from about 25 nm to about 250 nm, from about 25 nm to about 200 nm, fromabout 25 nm to about 150 nm, from about 25 nm to about 100 nm, fromabout 50 nm to about 500 nm, from about 75 nm to about 500 nm, fromabout 100 nm to about 500 nm, from about 150 nm to about 500 nm, fromabout 200 nm to about 500 nm, from about 250 nm to about 500 nm, or fromabout 300 nm to about 500 nm.

In some embodiments, the anti-reflection coating comprises a thicknessthat is greater than the surface thickness. The removal of the surfacethickness forms a surface defect 340 in that removal area, while theremaining coated surface 320 may form a pristine condition since thereis no surface defect present.

In some embodiments, as shown in FIG. 3, the anti-reflection coating 300includes a multi-layer coating that includes at least two layers suchthat a first layer 311 is disposed on the substrate surface 220 and asecond layer 312 is disposed on the first layer 311. The second layer312 may have a layer thickness 314 that is less than the surfacethickness 360. In other words, the surface thickness 360 is greater thanor equal to the layer thickness 314 of the second layer 312 such thatremoval of the surface thickness 360 includes removal of at least aportion of the second layer 312 from the coated surface 320. In suchembodiments, the coated surface 320 includes areas formed from thesecond layer, which may provide a pristine condition, and areas formedfrom the first layer 311, which comprise a surface defect 340.

As shown in FIG. 4, the surface defect 340 of one or more embodimentsmay include the addition of a material or contaminant 365 to the coatedsurface 320 of the anti-reflection coating 300 (e.g., fingerprints,fingerprint residue(s) or fingerprint-simulating medium or media). Insome embodiments, the contaminant 365 may be present as a planar layerhaving a thickness in the range from about 100 nm to about 2000 nm. Inspecific embodiments, the thickness is intended to simulate afingerprint droplet. The contaminant may have a refractive index in therange from about 1.4 to about 1.6, or about 1.49 to simulate oilscontained in fingerprint residue. In some embodiments, % R₁ and/or %R_(av1), and % R₂ and/or % R_(av2) may be measured using the sametechniques used to measure reflectance where the surface defect includesremoval of a surface thickness or the addition of a contaminant. Inother embodiments having a surface defect including the addition of acontaminant, % R₁ and/or % R_(av1) may be measured or modeled when theanti-reflection coating is in an immersed stated or in or surrounded byair (i.e., % R₁ and/or % R_(av1) at the air/anti-reflection coatinginterface is captured by a reflectance measurement system). In suchembodiments, % R₂ and/or % R_(av2) may be measured or modeled when theanti-reflection coating is in an immersed state or in or surrounded bythe contaminant (i.e., % R₂ and/or % R_(av2) at the air/contaminantinterface is captured by a reflectance measurement system butreflectance from any air interfaces in system is removed or subtractedout). The detector or measurement system lens may be in contact with acontaminant bath that is also surrounding the coated surface of thearticle.

In one or more embodiments, % R_(av2) may be equal to or less than %R_(av1). In one or more embodiments % R_(av1) may be in the range fromabout 0.5% to about 7%, or from about 0.6% to about 6.0%, over theentire visible spectrum or at least a portion of the visible spectrum.In one or more embodiments, % R_(av2) may be about 10% or less (e.g.,about 8% or less, about 6% or less, about 5% or less, about 4% or less,about 3% or less, or about 2% or less) or in the range from about 0.1%to about 8%, over the entire visible spectrum or at least a portion ofthe visible spectrum. Where the surface defect includes the addition ofa contaminant, the % R_(av2) may be about 2% or less, 1% or less, orabout 0.5% or less, across at least a portion of the visible spectrum.

At least one of % R₁ and % R₂ may exhibit oscillations over the visiblespectrum over which the reflectance was measured. At least one of % R₁and % R₂ may include an average oscillation amplitude of about 2%absolute reflectance or less, over the visible spectrum. As used herein,the term “amplitude” includes the peak-to-valley change in reflectance(or transmittance) over the visible spectrum or a given wavelengthwidth. The phrase “average oscillation amplitude” includes thepeak-to-valley change in reflectance or transmittance averaged overevery possible 100 nm wavelength range within the visible spectrum orover a given wavelength width. In some embodiments, the averageoscillation amplitude may be about 1.75% or less, about 1.5% or less,about 1% or less, about 0.75% or less, about 0.5% or less, about 0.25%or less, or about 0.1% or less, in absolute reflectance terms, over theentire visible spectrum or a given wavelength width of about 100 nm. Insome instances, the lower limit of the average oscillation amplitude maybe about 0.1%. Accordingly, the average oscillation amplitude of atleast one of % R₁ and % R₂ may be in the range from about 0.1% to about2%, in absolute reflectance terms, over the entire visible spectrum or agiven wavelength width of about 100 nm. The degree of oscillation mayalso be described in terms of a percent relative to an averagereflectance or transmittance value, across the visible spectrum or overa given wavelength width. For example, at least one of % R₁ and % R₂ mayexhibit reflectance oscillations of less than about 30%, less than about20% or less than about 10%, relative to a mean reflectance value, overthe visible spectrum or a given wavelength width. In one or moreembodiments, where the surface defect includes the addition of acontaminant, the coated surface exhibits a maximum reflectance value ofabout 8% or less across the visible spectrum and optionally includes amaximum oscillation amplitude of about 7.5% absolute reflectance or less(e.g., about 6%, 5% or about 4% absolute reflectance or less), acrossthe visible spectrum.

In one or more embodiments, the coated surface comprises a contrastratio measured as the ratio of the second average reflectance to thefirst average reflectance (% R_(av2):% R_(av1)), over the visiblespectrum or a given wavelength width, provided that % R_(av2) and %R_(av1) are measured at the same incident illumination angle. In one ormore embodiments, the contrast ratio may be in the range from about 0.5to about 50. For example, the contrast ratio may be in the range fromabout 0.5 to about 45, from about 0.5 to about 40, from about 0.5 toabout 35, from about 0.5 to about 30, from about 0.5 to about 25, fromabout 0.5 to about 20, from about 0.5 to about 15, from about 0.5 toabout 10, from about 0.5 to about 8, from about 0.5 to about 6, or fromabout 0.5 to about 5. For comparison, known anti-reflection coatings,which have a surface defect of about 25 nm to about 500 nm surfacethickness removed, typically exhibit a contrast ratio of about 100 orgreater. In some instances, the contrast ratio of the anti-reflectioncoating may be related to the surface defect. For example, when thesurface defect includes up to about 25 nm of surface thickness removal,the contrast ratio may be about 10 or less, about 5 or less or about 2or less (with the lower limit being about 0.5); and the % R_(av2) mayabout 6% or less, 4% or less, or 3% or less. In another example, whenthe surface defect includes up to about 50 nm of surface thicknessremoval, the contrast ratio may be about 20 or less, 10 or less, about 5or less, about 3 or less, or about 2 or less (with the lower limit beingabout 0.5); and the % R_(av2) may about 8% or less, about 6% or less, orabout 5% or less. In yet another example, when the surface defectincludes up to about 100 nm of surface thickness removal, the contrastratio may be about 50 or less, 20 or less, 10 or less, about 5 or less,or about 3 or less (with the lower limit being about 0.5); and the %R_(av2) may about 12% or less, about 8% or less, about 7% or less, orabout 6% or less. In another example, when the surface defect includesup to about 500 nm of surface thickness removal, the contrast ratio maybe about 50 or less, 20 or less, 10 or less, about 5 or less, or about 3or less (with the lower limit being about 0.5); and the % R_(av2) mayabout 12% or less. In embodiments in which the surface defect includesthe addition of a contaminant, the contrast ratio may be about 20 orless, about 10 or less, about 8 or less, about 6 or less, about 5 orless, about 4 or less, about 3 or less, about 2 or less (with the lowerlimit being about 0.5). Such contrast ratio and/or % R_(av2) values maybe along a visible spectrum in the range from about 400 nm to about 700nm, or from about 450 nm to about 650 nm.

In one or more embodiments, the contrast ratio of the coated surface mayexhibit oscillations. In some embodiments where the surface defectincludes the removal of a surface thickness, the contrast ratio has anaverage oscillation amplitude of about 2 or less, about 1 or less orabout 0.5 or less, in absolute ratio units, over the visible spectrum ora given wavelength width. In some embodiments where the surface defectincludes the addition of a contaminant, the contrast ratio has anaverage oscillation amplitude of about 10 or less, about 7 or less orabout 5 or less, in absolute ratio units, over the visible spectrum or agiven wavelength width.

The performance of the anti-reflection coating 300 of one or moreembodiments may be described in terms of the change in color inreflectance or transmittance of the article. The color may berepresented by color values or coordinates (a*, b*) under theInternational Commission on Illumination (“CIE”) L*, a*, b* colorimetrysystem. The change in color may be described as a color shift asdetermined by the following equation √(a*₂−a*₁)²+(b*₂−b*₁)²), using thea* and b* coordinates of the coated surface. The coordinates a*₁, andb*₁ may be the color coordinates 1) of the coated surface in pristinecondition or at areas where the coated surface is in a pristine; 2) (0,0); or 3) a reference color coordinate. The coordinates a*₂, and b*₂ maybe the color coordinates of the coated surface after formation of asurface defect or at areas including a surface defect. When measuringthe color coordinates (a*₁, b*₁) and (a*₂, b*₂), the incidentillumination angle and the illuminant are the same. In some embodiments,the color shift may be described as Δa*b* and may about 6 or less at theincident illumination angles described herein (e.g., from about 0degrees to about 75 degrees, from about 0 degrees to about 30 degrees orfrom about 30 degrees to about 75 degrees) and under the illuminantsdescribed herein. In some embodiments, the color shift may be about 5.5or less, about 5 or less, about 4.5 or less, about 4 or less, about 3.5or less, about 3 or less, about 2.5 or less, about 2 or less, about 1.9or less, 1.8 or less, 1.7 or less, 1.6 or less, 1.5 or less, 1.4 orless, 1.3 or less, 1.2 or less, 1.1 or less, 1 or less, 0.9 or less, 0.8or less, 0.7 or less, 0.6 or less, 0.5 or less, 0.4 or less, 0.3 orless, 0.2 or less, or 0.1 or less. In some embodiments, the color shiftmay be about 0. In some embodiments, the coated surface exhibits suchcolor shift ranges when the surface defect includes removal of a surfacethickness in the range from about 0.1 nm to about 200 nm, or from about0.1 nm to about 150 nm, or from about 0.1 nm to about 140 nm. In one ormore specific embodiments, the color shift is about 3 or less, when theincident illumination angle is about 60 degrees and the surfacethickness is in a range from about 0.1 to about 100 nm.

In one or more embodiments, the anti-reflection coating may include morethan one layer. In some instances, the anti-reflection coating mayinclude a first layer 311 disposed on the substrate surface 220 and asecond layer 312 disposed on the first layer, wherein the first layer311 comprises a high refractive index material (e.g., having arefractive index that is greater than the refractive index of the secondlayer 312). In some instances, the first layer 311 may have a thicknessof about 50 nm or less. In some embodiments, more than one, or even allof the layers of the anti-reflection coating including a high refractiveindex material may be have a thickness of about 100 nm or less or about50 nm or less.

The anti-reflection coating 300 and/or the article 100 may be describedin terms of a hardness measured by a Berkovich Indenter Hardness Test.As used herein, the “Berkovich Indenter Hardness Test” includesmeasuring the hardness of a material on a surface thereof by indentingthe surface with a diamond Berkovich indenter. The Berkovich IndenterHardness Test includes indenting the coated surface 320 of the articleor the surface of the anti-reflection coating (or the surface of any oneor more of the layers in the anti-reflection coating, as describedherein) with the diamond Berkovich indenter to form an indent to anindentation depth in the range from about 50 nm to about 1000 nm (or theentire thickness of the anti-reflection coating or layer, whichever isless) and measuring the maximum hardness from this indentation along theentire indentation depth range or a segment of this indentation depth(e.g., in the range from about 100 nm to about 600 nm), generally usingthe methods set forth in Oliver, W. C.; Pharr, G. M. An improvedtechnique for determining hardness and elastic modulus using load anddisplacement sensing indentation experiments. J. Mater. Res., Vol. 7,No. 6, 1992, 1564-1583; and Oliver, W. C.; Pharr, G. M. Measurement ofHardness and Elastic Modulus by Instrument Indentation: Advances inUnderstanding and Refinements to Methodology. J. Mater. Res., Vol. 19,No. 1, 2004, 3-20. As used herein, hardness refers to a maximumhardness, and not an average hardness.

In some embodiments, the anti-reflection coating 300 may exhibit ahardness of greater than about 5 GPa, as measured on the coated surface320, by the Berkovitch Indenter Hardness Test. The anti-reflectioncoating may exhibit a hardness of about 8 GPa or greater, about 10 GPaor greater or about 12 GPa or greater. The article 100, including theanti-reflection coating 300 and any additional coatings, as describedherein, may exhibit a hardness of about 5 GPa or greater, about 8 GPa orgreater, about 10 GPa or greater or about 12 GPa or greater, as measuredon the coated surface 320, by the Berkovitch Indenter Hardness Test.Such measured hardness values may be exhibited by the anti-reflectioncoating 300 and/or the article 100 along an indentation depth of about50 nm or greater or about 100 nm or greater (e.g., from about 100 nm toabout 300 nm, from about 100 nm to about 400 nm, from about 100 nm toabout 500 nm, from about 100 nm to about 600 nm, from about 200 nm toabout 300 nm, from about 200 nm to about 400 nm, from about 200 nm toabout 500 nm, or from about 200 nm to about 600 nm).

The anti-reflection coating 300 may have at least one layer having ahardness (as measured on the surface of such layer of about 5 GPa orgreater, 8 GPa or greater, 10 GPa or greater, 12 GPa or greater, about13 GPa or greater, about 14 GPa or greater, about 15 GPa or greater,about 16 GPa or greater, about 17 GPa or greater, about 18 GPa orgreater, about 19 GPa or greater, about 20 GPa or greater, about 22 GPaor greater, about 23 GPa or greater, about 24 GPa or greater, about 25GPa or greater, about 26 GPa or greater, or about 27 GPa or greater (upto about 50 GPa), as measured by the Berkovich Indenter Hardness Test.The hardness of such layer may be in the range from about 18 GPa toabout 21 GPa, as measured by the Berkovich Indenter Hardness Test. Insome embodiments, the anti-reflection coating includes a hard materialhaving an average hardness of greater than about 5 GPa (e.g., about 10GPa or greater, about 15 GPa or greater, or about 20 GPa or greater), asmeasured by a Berkovich Indenter Hardness Test, as defined herein. Thehard material may be present in all the layers of the anti-reflectioncoating or in one or more specific layers of the anti-reflectioncoating. In some instances, the anti-reflection coating may include alayer having a thickness of about 1 μm or greater, or about 2 μm orgreater that includes the hard material. Such measured hardness valuesmay be exhibited by the at least one layer along an indentation depth ofabout 50 nm or greater or 100 nm or greater (e.g., from about 100 nm toabout 300 nm, from about 100 nm to about 400 nm, from about 100 nm toabout 500 nm, from about 100 nm to about 600 nm, from about 200 nm toabout 300 nm, from about 200 nm to about 400 nm, from about 200 nm toabout 500 nm, or from about 200 nm to about 600 nm). In one or moreembodiments, the article exhibits a hardness that is greater than thehardness of the substrate (which can be measured on the opposite surfacefrom the coated surface).

In one or more embodiments, the anti-reflection coating 300 orindividual layers within the anti-reflection coating may exhibit anelastic modulus of about 75 GPa or greater, about 80 GPa or greater orabout 85 GPa or greater, as measured on the coated surface 320, byindenting that surface with a Berkovitch indenter. These modulus valuesmay represent a modulus measured very close to the coated surface 101,e.g. at indentation depths of 0-50 nm, or it may represent a modulusmeasured at deeper indentation depths, e.g. from about 50-1000 nm.

The anti-reflection coating may include a refractive index gradientalong at least a portion of its thickness, as described in U.S. patentapplication Ser. No. 14/262,224, filed on Apr. 25, 2014, entitled“Scratch-Resistant Articles with a Gradient Layer”, the contents ofwhich are incorporated herein by reference. Specifically, theanti-reflection coating may include a refractive index that increasesfrom a first surface (adjacent to the substrate surface 220) to thesecond surface (i.e., the coated surface). The refractive index mayincrease along the refractive index gradient at an average rate in therange from about 0.2/μm to about 0.5/μm and may be in the range fromabout 1.5 to about 2.0. The anti-reflection coating may include acompositional gradient that includes at least two of Si, Al, N, and O.

In other embodiments, the anti-reflective coating may include one morelayers that have different and optionally alternating refractiveindices, as described in U.S. patent application Ser. No. 14/262,066,filed on Apr. 25, 2014, entitled “Low-Color Scratch-Resistant Articleswith a Multilayer Optical Film,” the contents of which are incorporatedherein by reference. Specifically, the anti-reflection coating mayinclude a first low refractive index (RI) sub-layer and a second high RIsub-layer. An optional third sub-layer may also be included. In one ormore embodiments, the anti-reflection coating may include a plurality ofsub-layer sets. A single sub-layer set may include a first low RIsub-layer, a second high RI sub-layer and optionally, a third sub-layer.In some embodiments, the anti-reflection coating may include a pluralityof sub-layer sets such that the first low RI sub-layer (designated forillustration as “L”) and the second high RI sub-layer (designated forillustration as “H”) may be provide the following sequence ofsub-layers: L/H/L/H or H/L/H/L, such that the first low RI sub-layer andthe second high RI sub-layer appear to alternate along the physicalthickness of the optical interference layer. In some examples, theanti-reflection coating may have three sub-layer sets or up to 10sub-layer sets. For example, the anti-reflection coating may includefrom about 2 to about 12 sub-layer sets, from about 3 to about 8sub-layer sets, from about 3 to about 6 sub-layer sets. The thirdsub-layer(s) used in some examples may have a low RI, a high RI or amedium RI. In some embodiments, the third sub-layer(s) may have the sameRI as the first low RI sub-layer or the second high RI sub-layer. Inother embodiments, the third sub-layer(s) may have a medium RI that isbetween the RI of the first low RI sub-layer and the RI of the secondhigh RI sub-layer. The third sub-layer(s) may be disposed between theplurality of sub-layer sets and a functional coating (as will bedescribed herein) (not shown) or between the substrate and the pluralityof sub-layer sets (not shown). Alternatively, the third sub-layer may beincluded in the plurality of sub-layer sets (not shown). The thirdsub-layer may be provided in the anti-reflection coating in thefollowing exemplary configurations: L_(third sub-layer)/H/L/H/L;H_(third sub-layer)/L/H/L/H; L/H/L/H/L_(third sub-layer);H/L/H/L/H_(third sub-layer);L_(third sub-layer)/H/L/H/L/H_(third sub-layer);H_(third sub-layer)/L/H/L/H/L_(third sub-layer);L_(third sub-layer)/L/H/L/H; H_(third sub-layer)/H/L/H/L;H/L/H/L/L_(third sub-layer); L/H/L/H/H_(third sub-layer);L_(third sub-layer)/L/H/L/H/H_(third sub-layer);H_(third sub-layer)//H/L/H/L/L_(third sub-layer); L/M/H/L/M/H;H/M/L/H/M/L; M/L/H/L/M; and other combinations. In these configurations,“L” without any subscript refers to the first low RI sub-layer and “H”without any subscript refers to the second high RI sub-layer. Referenceto “L_(third sub-layer)” refers to a third sub-layer having a low RI,“H_(third sub-layer)” refers to a third sub-layer having a high RI and“M” refers to a third sub-layer having a medium RI.

As used herein, the terms “low RI”, “high RI” and “medium RI” refer tothe relative values for the RI to another (e.g., low RI<medium RI<highRI). In one or more embodiments, the term “low RI” when used with thefirst low RI sub-layer or with the third sub-layer, includes a rangefrom about 1.3 to about 1.7. In one or more embodiments, the term “highRI” when used with the second high RI sub-layer or with the thirdsub-layer, includes a range from about 1.6 to about 2.5. In someembodiments, the term “medium RI” when used with the third sub-layer,includes a range from about 1.55 to about 1.8. In some instances, theranges for low RI, high RI and medium RI may overlap; however, in mostinstances, the sub-layers of the optical interference layer have thegeneral relationship regarding RI of: low RI<medium RI<high RI.

Exemplary materials suitable for use in the anti-reflection coatinginclude: SiO₂, Al₂O₃, GeO₂, SiO, AlOxNy, AlN, Si₃N₄, SiO_(x)N_(y),Si_(u)Al_(v)O_(x)N_(y), Ta₂O₅, Nb₂O₅, TiO₂, ZrO₂, TiN, MgO, MgF₂, BaF₂,CaF₂, SnO₂, HfO₂, Y₂O₃, MoO₃, DyF₃, YbF₃, YF₃, CeF₃, polymers,fluoropolymers, plasma-polymerized polymers, siloxane polymers,silsesquioxanes, polyimides, fluorinated polyimides, polyetherimide,polyethersulfone, polyphenylsulfone, polycarbonate, polyethyleneterephthalate, polyethylene naphthalate, acrylic polymers, urethanepolymers, polymethylmethacrylate, other materials cited below assuitable for use in a scratch-resistant layer, and other materials knownin the art. Some examples of suitable materials for use in the first lowRI sub-layer include SiO₂, Al₂O₃, GeO₂, SiO, AlO_(x)N_(y), SiO_(x)N_(y),Si_(u)Al_(v)O_(x)N_(y), MgO, MgF₂, BaF₂, CaF₂, DyF₃, YbF₃, YF₃, andCeF₃. Some examples of suitable materials for use in the second high RIsub-layer include Si_(u)Al_(v)O_(x)N_(y), Ta₂O₅, Nb₂O₅, AlN, Si₃N₄,AlO_(x)N_(y), SiO_(x)N_(y), HfO₂, TiO₂, ZrO₂, Y₂O₃, Al₂O₃, and MoO₃.

In one or more embodiments at least one of the sub-layer(s) may includea specific optical thickness range. As used herein, the term “opticalthickness” is determined by (n*d), where “n” refers to the RI of thesub-layer and “d” refers to the physical thickness of the sub-layer. Inone or more embodiments, at least one of the sub-layers of theanti-reflection coating may include an optical thickness in the rangefrom about 2 nm to about 200 nm, from about 10 nm to about 100 nm, orfrom about 15 nm to about 100 nm. In some embodiments, all of thesub-layers in the anti-reflection coating may each have an opticalthickness in the range from about 2 nm to about 200 nm, from about 10 nmto about 100 nm or from about 15 nm to about 100 nm. In some cases, atleast one sub-layer of the anti-reflection coating has an opticalthickness of about 50 nm or greater. In some cases, each of the firstlow RI sub-layers have an optical thickness in the range from about 2 nmto about 200 nm, from about 10 nm to about 100 nm, or from about 15 nmto about 100 nm. In other cases, each of the second high RI sub-layershave an optical thickness in the range from about 2 nm to about 200 nm,from about 10 nm to about 100 nm, or from about 15 nm to about 100 nm.In yet other cases, each of the third sub-layers have an opticalthickness in the range from about 2 nm to about 200 nm, from about 10 nmto about 100 nm, or from about 15 nm to about 100 nm.

In one or more embodiments, the anti-reflection coating has a physicalthickness of about 800 nm or less. The anti-reflection coating may havea physical thickness in the range from about 10 nm to about 800 nm, fromabout 50 nm to about 800 nm, from about 100 nm to about 800 nm, fromabout 150 nm to about 800 nm, from about 200 nm to about 800 nm, fromabout 10 nm to about 750 nm, from about 10 nm to about 700 nm, fromabout 10 nm to about 650 nm, from about 10 nm to about 600 nm, fromabout 10 nm to about 550 nm, from about 10 nm to about 500 nm, fromabout 10 nm to about 450 nm, from about 10 nm to about 400 nm, fromabout 10 nm to about 350 nm, from about 10 nm to about 300 nm, fromabout 50 to about 300, and all ranges and sub-ranges therebetween

The substrate 200 may include an amorphous substrate, a crystallinesubstrate or a combination thereof. The substrate 200 may be formed fromman-made materials and/or naturally occurring materials. In somespecific embodiments, the substrate 200 may specifically exclude plasticand/or metal substrates. In one or more embodiments, the substrateexhibits a refractive index in the range from about 1.45 to about 1.55.In specific embodiments, the substrate 200 may exhibit an averagestrain-to-failure at a surface on one or more opposing major surfacethat is 0.5% or greater, 0.6% or greater, 0.7% or greater, 0.8% orgreater, 0.9% or greater, 1% or greater, 1.1% or greater, 1.2% orgreater, 1.3% or greater, 1.4% or greater 1.5% or greater or even 2% orgreater, as measured using ball-on-ring testing using at least 5, atleast 10, at least 15, or at least 20 samples. In specific embodiments,the substrate 200 may exhibit an average strain-to-failure at itssurface on one or more opposing major surface of about 1.2%, about 1.4%,about 1.6%, about 1.8%, about 2.2%, about 2.4%, about 2.6%, about 2.8%,or about 3% or greater. Suitable substrates 110 may exhibit an elasticmodulus (or Young's modulus) in the range from about 30 GPa to about 120GPa.

In one or more embodiments, the amorphous substrate may include glass,which may be strengthened or non-strengthened. Examples of suitableglass include soda lime glass, alkali aluminosilicate glass, alkalicontaining borosilicate glass and alkali aluminoborosilicate glass. Insome variants, the glass may be free of lithia. In one or morealternative embodiments, the substrate 200 may include crystallinesubstrates such as glass ceramic substrates (which may be strengthenedor non-strengthened) or may include a single crystal structure, such assapphire. In one or more specific embodiments, the substrate 200includes an amorphous base (e.g., glass) and a crystalline cladding(e.g., sapphire layer, a polycrystalline alumina layer and/or or aspinel (MgAl₂O₄) layer).

The substrate 200 may be substantially planar or sheet-like, althoughother embodiments may utilize a curved or otherwise shaped or sculptedsubstrate. The substrate 200 may be substantially optically clear,transparent and free from light scattering. In such embodiments, thesubstrate may exhibit an average transmittance over the opticalwavelength regime of about 85% or greater, about 86% or greater, about87% or greater, about 88% or greater, about 89% or greater, about 90% orgreater, about 91% or greater or about 92% or greater.

Additionally or alternatively, the physical thickness of the substrate200 may vary along one or more of its dimensions for aesthetic and/orfunctional reasons. For example, the edges of the substrate 200 may bethicker as compared to more central regions of the substrate 200. Thelength, width and physical thickness dimensions of the substrate 200 mayalso vary according to the application or use of the article 100.

The substrate 200 may be provided using a variety of differentprocesses. For instance, where the substrate 200 includes an amorphoussubstrate such as glass, various forming methods can include float glassprocesses and down-draw processes such as fusion draw and slot draw.

Once formed, a substrate 200 may be strengthened to form a strengthenedsubstrate. As used herein, the term “strengthened substrate” may referto a substrate that has been chemically strengthened, for examplethrough ion-exchange of larger ions for smaller ions in the surface ofthe substrate. However, other strengthening methods known in the art,such as thermal tempering, or utilizing a mismatch of the coefficient ofthermal expansion between portions of the substrate to createcompressive stress and central tension regions, may be utilized to formstrengthened substrates.

Where the substrate is chemically strengthened by an ion exchangeprocess, the ions in the surface layer of the substrate are replacedby—or exchanged with—larger ions having the same valence or oxidationstate. Ion exchange processes are typically carried out by immersing asubstrate in a molten salt bath containing the larger ions to beexchanged with the smaller ions in the substrate. It will be appreciatedby those skilled in the art that parameters for the ion exchangeprocess, including, but not limited to, bath composition andtemperature, immersion time, the number of immersions of the substratein a salt bath (or baths), use of multiple salt baths, additional stepssuch as annealing, washing, and the like, are generally determined bythe composition of the substrate and the desired compressive stress(CS), depth of compressive stress layer (or depth of layer) of thesubstrate that result from the strengthening operation. By way ofexample, ion exchange of alkali metal-containing glass substrates may beachieved by immersion in at least one molten bath containing a salt suchas, but not limited to, nitrates, sulfates, and chlorides of the largeralkali metal ion. The temperature of the molten salt bath typically isin a range from about 380° C. up to about 450° C., while immersion timesrange from about 15 minutes up to about 40 hours. However, temperaturesand immersion times different from those described above may also beused.

In addition, non-limiting examples of ion exchange processes in whichglass substrates are immersed in multiple ion exchange baths, withwashing and/or annealing steps between immersions, are described in U.S.patent application Ser. No. 12/500,650, filed Jul. 10, 2009, by DouglasC. Allan et al., entitled “Glass with Compressive Surface for ConsumerApplications” and claiming priority from U.S. Provisional PatentApplication No. 61/079,995, filed Jul. 11, 2008, in which glasssubstrates are strengthened by immersion in multiple, successive, ionexchange treatments in salt baths of different concentrations; and U.S.Pat. No. 8,312,739, by Christopher M. Lee et al., issued on Nov. 20,2012, and entitled “Dual Stage Ion Exchange for Chemical Strengtheningof Glass,” and claiming priority from U.S. Provisional PatentApplication No. 61/084,398, filed Jul. 29, 2008, in which glasssubstrates are strengthened by ion exchange in a first bath is dilutedwith an effluent ion, followed by immersion in a second bath having asmaller concentration of the effluent ion than the first bath. Thecontents of U.S. patent application Ser. No. 12/500,650 and U.S. Pat.No. 8,312,739 are incorporated herein by reference in their entirety.

The degree of chemical strengthening achieved by ion exchange may bequantified based on the parameters of central tension (CT), surface CS,and depth of layer (DOL). Surface CS may be measured near the surface orwithin the strengthened glass at various depths. A maximum CS value mayinclude the measured CS at the surface (CS_(s)) of the strengthenedsubstrate. The CT, which is computed for the inner region adjacent thecompressive stress layer within a glass substrate, can be calculatedfrom the CS, the physical thickness t, and the DOL. CS and DOL aremeasured using those means known in the art. Such means include, but arenot limited to, measurement of surface stress (FSM) using commerciallyavailable instruments such as the FSM-6000, manufactured by Luceo Co.,Ltd. (Tokyo, Japan), or the like, and methods of measuring CS and DOLare described in ASTM 1422C-99, entitled “Standard Specification forChemically Strengthened Flat Glass,” and ASTM 1279.19779 “Standard TestMethod for Non-Destructive Photoelastic Measurement of Edge and SurfaceStresses in Annealed, Heat-Strengthened, and Fully-Tempered Flat Glass,”the contents of which are incorporated herein by reference in theirentirety. Surface stress measurements rely upon the accurate measurementof the stress optical coefficient (SOC), which is related to thebirefringence of the glass substrate. SOC in turn is measured by thosemethods that are known in the art, such as fiber and four point bendmethods, both of which are described in ASTM standard C770-98 (2008),entitled “Standard Test Method for Measurement of Glass Stress-OpticalCoefficient,” the contents of which are incorporated herein by referencein their entirety, and a bulk cylinder method. The relationship betweenCS and CT is given by the expression (1):

CT=(CS·DOL)/(t−2DOL)  (1),

wherein t is the physical thickness (μm) of the glass article. Invarious sections of the disclosure, CT and CS are expressed herein inmegaPascals (MPa), physical thickness t is expressed in eithermicrometers (μm) or millimeters (mm) and DOL is expressed in micrometers(μm).

In one embodiment, a strengthened substrate 200 can have a surface CS of250 MPa or greater, 300 MPa or greater, e.g., 400 MPa or greater, 450MPa or greater, 500 MPa or greater, 550 MPa or greater, 600 MPa orgreater, 650 MPa or greater, 700 MPa or greater, 750 MPa or greater or800 MPa or greater. The strengthened substrate may have a DOL of 10 μmor greater, 15 μm or greater, 20 μm or greater (e.g., 25 μm, 30 μm, 35μm, 40 μm, 45 μm, 50 μm or greater) and/or a CT of 10 MPa or greater, 20MPa or greater, 30 MPa or greater, 40 MPa or greater (e.g., 42 MPa, 45MPa, or 50 MPa or greater) but less than 100 MPa (e.g., 95, 90, 85, 80,75, 70, 65, 60, 55 MPa or less). In one or more specific embodiments,the strengthened substrate has one or more of the following: a surfaceCS greater than 500 MPa, a DOL greater than 15 μm, and a CT greater than18 MPa.

Example glasses that may be used in the substrate may include alkalialuminosilicate glass compositions or alkali aluminoborosilicate glasscompositions, though other glass compositions are contemplated. Suchglass compositions are capable of being chemically strengthened by anion exchange process. One example glass composition comprises SiO₂, B₂O₃and Na₂O, where (SiO₂+B₂O₃)≥66 mol. %, and Na₂O≥9 mol. %. In anembodiment, the glass composition includes at least 6 wt. % aluminumoxide. In a further embodiment, the substrate includes a glasscomposition with one or more alkaline earth oxides, such that a contentof alkaline earth oxides is at least 5 wt. %. Suitable glasscompositions, in some embodiments, further comprise at least one of K₂O,MgO, and CaO. In a particular embodiment, the glass compositions used inthe substrate can comprise 61-75 mol. % SiO2; 7-15 mol. % Al₂O₃; 0-12mol. % B₂O₃; 9-21 mol. % Na₂O; 0-4 mol. % K₂O; 0-7 mol. % MgO; and 0-3mol. % CaO.

A further example glass composition suitable for the substratecomprises: 60-70 mol. % SiO₂; 6-14 mol. % Al₂O₃; 0-15 mol. % B₂O₃; 0-15mol. % Li₂O; 0-20 mol. % Na₂O; 0-10 mol. % K₂O; 0-8 mol. % MgO; 0-10mol. % CaO; 0-5 mol. % ZrO₂; 0-1 mol. % SnO₂; 0-1 mol. % CeO₂; less than50 ppm As₂O₃; and less than 50 ppm Sb₂O₃; where 12 mol.%≤(Li₂O+Na₂O+K₂O)≤20 mol. % and 0 mol. %≤(MgO+CaO)≤10 mol. %.

A still further example glass composition suitable for the substratecomprises: 63.5-66.5 mol. % SiO₂; 8-12 mol. % Al₂O₃; 0-3 mol. % B₂O₃;0-5 mol. % Li₂O; 8-18 mol. % Na₂O; 0-5 mol. % K₂O; 1-7 mol. % MgO; 0-2.5mol. % CaO; 0-3 mol. % ZrO₂; 0.05-0.25 mol. % SnO₂; 0.05-0.5 mol. %CeO₂; less than 50 ppm As₂O₃; and less than 50 ppm Sb₂O₃; where 14 mol.%≤(Li₂O+Na₂O+K₂O)≤18 mol. % and 2 mol. %≤(MgO+CaO)≤7 mol. %.

In a particular embodiment, an alkali aluminosilicate glass compositionsuitable for the substrate comprises alumina, at least one alkali metaland, in some embodiments, greater than 50 mol. % SiO₂, in otherembodiments at least 58 mol. % SiO₂, and in still other embodiments atleast 60 mol. % SiO₂, wherein the ratio

${\frac{{{Al}_{2}O_{3}} + {B_{2}O_{3}}}{\Sigma \mspace{14mu} {modifiers}} > 1},$

where in the ratio the components are expressed in mol. % and themodifiers are alkali metal oxides. This glass composition, in particularembodiments, comprises: 58-72 mol. % SiO₂; 9-17 mol. % Al₂O₃; 2-12 mol.% B₂O₃; 8-16 mol. % Na₂O; and 0-4 mol. % K₂O, wherein the ratio

$\frac{{{Al}_{2}O_{3}} + {B_{2}O_{3}}}{\Sigma \mspace{14mu} {modifiers}} > 1.$

In still another embodiment, the substrate may include an alkalialuminosilicate glass composition comprising: 64-68 mol. % SiO₂; 12-16mol. % Na₂O; 8-12 mol. % Al₂O₃; 0-3 mol. % B₂O₃; 2-5 mol. % K₂O; 4-6mol. % MgO; and 0-5 mol. % CaO, wherein: 66 mol. %≤SiO₂+B₂O₃+CaO≤69 mol.%; Na₂O+K₂O+B₂O₃+MgO+CaO+SrO>10 mol. %; 5 mol. %≤MgO+CaO+SrO≤8 mol. %;(Na₂O+B₂O₃)—Al₂O₃≤2 mol. %; 2 mol. %≤Na₂O—Al₂O₃≤6 mol. %; and 4 mol.%≤(Na₂O+K₂O)—Al₂O₃≤10 mol. %.

In an alternative embodiment, the substrate may comprise an alkalialuminosilicate glass composition comprising: 2 mol % or more of Al₂O₃and/or ZrO₂, or 4 mol % or more of Al₂O₃ and/or ZrO₂.

Where the substrate 200 includes a crystalline substrate, the substratemay include a single crystal, which may include Al₂O₃. Such singlecrystal substrates are referred to as sapphire. Other suitable materialsfor a crystalline substrate include polycrystalline alumina layer and/orspinel (MgAl₂O₄).

Optionally, the crystalline substrate 200 may include a glass ceramicsubstrate, which may be strengthened or non-strengthened. Examples ofsuitable glass ceramics may include Li₂O—Al₂O₃—SiO₂ system (i.e.LAS-System) glass ceramics, MgO—Al₂O₃—SiO₂ system (i.e. MAS-System)glass ceramics, and/or glass ceramics that include a predominant crystalphase including β-quartz solid solution, β-spodumene ss, cordierite, andlithium disilicate. The glass ceramic substrates may be strengthenedusing the chemical strengthening processes disclosed herein. In one ormore embodiments, MAS-System glass ceramic substrates may bestrengthened in Li₂SO₄ molten salt, whereby an exchange of 2Li⁺ for Mg²⁺can occur.

The substrate 200 according to one or more embodiments can have aphysical thickness ranging from about 100 μm to about 5 mm. Examplesubstrate 200 physical thicknesses range from about 100 μm to about 500μm (e.g., 100, 200, 300, 400 or 500 μm). Further example substrate 200physical thicknesses range from about 500 μm to about 1000 μm (e.g.,500, 600, 700, 800, 900 or 1000 μm). The substrate 200 may have aphysical thickness greater than about 1 mm (e.g., about 2, 3, 4, or 5mm). In one or more specific embodiments, the substrate 200 may have aphysical thickness of 2 mm or less or less than 1 mm. The substrate 200may be acid polished or otherwise treated to remove or reduce the effectof surface flaws.

The articles described herein may incorporate other coatings with theanti-reflection coating. For example, one or more scratch-resistantcoatings, anti-fingerprint coatings, anti-microbial coatings and othersuch functional coatings, may be incorporated into the article. In otherexamples, more than one anti-reflection coating may be used incombination with the functional coating(s). For example, theanti-reflection coating may be present on top of a function coating suchthat the anti-reflection coating forms the top coating of the article.In another example, an anti-reflection coating may be present underneaththe functional coating and another anti-reflection coating may bepresent on top of the functional coating.

The anti-reflection coating and/or other coatings may be formed usingvarious deposition methods such as vacuum deposition techniques, forexample, chemical vapor deposition (e.g., plasma enhanced chemical vapordeposition, low-pressure chemical vapor deposition, atmospheric pressurechemical vapor deposition, and plasma-enhanced atmospheric pressurechemical vapor deposition), physical vapor deposition (e.g., reactive ornonreactive sputtering or laser ablation), thermal or e-beam evaporationand/or atomic layer deposition. One or more layers of theanti-reflection coating may include nano-pores or mixed-materials toprovide specific refractive index ranges or values.

EXAMPLES

Various embodiments will be further clarified by the following examples.

Examples 1-10 used modeling to understand the reflectance spectra ofarticles in which the anti-reflection coating is pristine and includes asurface defect. The modeling was based on collected refractive indexdata from formed layers of various materials that may be used in theanti-reflection coatings and a substrate of either strengthenedaluminoborosilicate (“ABS”) glass or sapphire. The layers of theanti-reflection coating were formed by DC reactive sputtering, reactiveDC and radio frequency (RF) sputtering, and e-beam evaporation ontosilicon wafers. Some of the formed layers included SiO₂, Nb₂O₅, or Al₂O₃and were deposited onto silicon wafers by DC reactive sputtering from asilicon, niobium or aluminum target (respectively) at a temperature ofabout 50° C. using ion assist. Layers formed in this manner aredesignated with the indicator “RS”. Layers of Si_(u)Al_(v)O_(x)N_(y)were deposited onto silicon wafers by DC reactive sputtering combinedwith RF superimposed DC sputtering, with ion assist using a sputterdeposition tool supplied by AJA-Industries. The wafer was heated to 200°C. during deposition and silicon targets having a 3 inch diameter and analuminum targets having a 3 inch diameter were used. Reactive gases usedincluded nitrogen and oxygen and argon was used as the inert gas. The RFpower was supplied to the silicon target at 13.56 Mhz and DC power wassupplied to the aluminum target. The resulting Si_(u)Al_(v)O_(x)N_(y)layers had a refractive index at 550 nm of about 1.95 and a measuredhardness of greater than about 15 GPa, using a Berkovitch indenter onthe surface of the Si_(u)Al_(v)O_(x)N_(y) layer being tested, asdescribed herein. Si_(u)Al_(v)O_(x)N_(y) and AlO_(x)N_(y) materials weredeposited and had very similar hardness and refractive index profiles.Accordingly, Si_(u)Al_(v)O_(x)N_(y) and AlO_(x)N_(y) materials may bereadily interchanged for one another.

The refractive indices (as a function of wavelength) of the formedlayers of the optical film and the substrates were measured usingspectroscopic ellipsometry. Tables 1-6 include the refractive indicesand dispersion curves measured. The refractive indices thus measuredwere then used to calculate reflectance spectra for modeled Examples1-10.

TABLE 1 Refractive indices and dispersion curve for a RS-SiO₂ layer vs.wavelength. Material Reactive sputtered SiO₂ Wavelength (nm) RefractiveIndex (n) Extinction Coefficient (k) 246.5 1.52857 0.0 275.2 1.51357 0.0300.8 1.50335 0.0 324.7 1.49571 0.0 350.2 1.48911 0.0 375.8 1.48374 0.0399.7 1.47956 0.0 425.2 1.47583 0.0 450.7 1.47269 0.0 476.3 1.47002 0.0500.2 1.46788 0.0 525.7 1.46589 0.0 549.5 1.46427 0.0 575.0 1.46276 0.0600.5 1.46143 0.0 625.9 1.46026 0.0 649.7 1.45928 0.0 675.1 1.45835 0.0700.5 1.45751 0.0 725.9 1.45676 0.0 751.3 1.45609 0.0 775.0 1.45551 0.0800.4 1.45496 0.0 850.9 1.45399 0.0 899.8 1.45320 0.0 950.2 1.45252 0.0999.0 1.45195 0.0 1100.0 1.45100 0.0 1199.6 1.45028 0.0 1302.0 1.449710.0 1400.8 1.44928 0.0 1499.7 1.44892 0.0 1599.0 1.44863 0.0 1688.41.44841 0.0

TABLE 2 Refractive indices and dispersion curve for aSi_(u)Al_(v)O_(x)N_(y) layer vs. wavelength. Material Reactive sputteredSi_(u)Al_(v)O_(x)N_(y) or AlO_(x)N_(y) Wavelength (nm) Refractive Index(n) Extinction Coefficient (k) 206.6 2.37659 0.21495 225.4 2.285240.11270 251.0 2.18818 0.04322 275.5 2.12017 0.01310 300.9 2.069160.00128 324.6 2.03698 0.0 350.2 2.01423 0.0 360.4 2.00718 0.0 371.22.00059 0.0 380.3 1.99562 0.0 389.9 1.99090 0.0 400.0 1.98640 0.0 410.51.98213 0.0 421.7 1.97806 0.0 430.5 1.97513 0.0 439.7 1.97230 0.0 449.21.96958 0.0 459.2 1.96695 0.0 469.6 1.96441 0.0 480.6 1.96197 0.0 492.01.95961 0.0 499.9 1.95808 0.0 512.3 1.95586 0.0 520.9 1.95442 0.0 529.91.95301 0.0 539.1 1.95165 0.0 548.6 1.95031 0.0 558.5 1.94900 0.0 568.71.94773 0.0 579.4 1.94649 0.0 590.4 1.94528 0.0 601.9 1.94410 0.0 613.81.94295 0.0 619.9 1.94239 0.0 632.6 1.94128 0.0 639.1 1.94074 0.0 652.61.93968 0.0 666.6 1.93864 0.0 681.2 1.93763 0.0 696.5 1.93665 0.0 712.61.93569 0.0 729.3 1.93477 0.0 746.9 1.93386 0.0 765.3 1.93299 0.0 784.71.93214 0.0 805.1 1.93131 0.0 826.6 1.93051 0.0 849.2 1.92973 0.0 873.11.92898 0.0 898.4 1.92825 0.0 925.3 1.92754 0.0 953.7 1.92686 0.0 999.91.92587 0.0 1050.7 1.92494 0.0

TABLE 3 Refractive indices and dispersion curve for ABS glass substratevs. wavelength. Material Aluminosilicate glass Wavelength (nm)Refractive Index (n) Extinction Coefficient (k) 350.6 1.53119 0.0 360.71.52834 0.0 370.8 1.52633 0.0 380.8 1.52438 0.0 390.9 1.52267 0.0 400.91.52135 0.0 411.0 1.52034 0.0 421.0 1.51910 0.0 431.1 1.51781 0.0 441.11.51686 0.0 451.2 1.51600 0.0 461.2 1.51515 0.0 471.2 1.51431 0.0 481.31.51380 0.0 491.3 1.51327 0.0 501.3 1.51259 0.0 511.4 1.51175 0.0 521.41.51124 0.0 531.4 1.51082 0.0 541.5 1.51040 0.0 551.5 1.50999 0.0 561.51.50959 0.0 571.5 1.50918 0.0 581.6 1.50876 0.0 591.6 1.50844 0.0 601.61.50828 0.0 611.6 1.50789 0.0 621.7 1.50747 0.0 631.7 1.50707 0.0 641.71.50667 0.0 651.7 1.50629 0.0 661.7 1.50591 0.0 671.8 1.50555 0.0 681.81.50519 0.0 691.8 1.50482 0.0 701.8 1.50445 0.0 709.8 1.50449 0.0 719.81.50456 0.0 729.9 1.50470 0.0 739.9 1.50484 0.0 749.9 1.50491 0.0

TABLE 4 Refractive indices and dispersion curve for sapphire substratevs. wavelength. Material Sapphire Wavelength (nm) Refractive Index (n)Extinction Coefficient (k) 206.6 1.83400 0.0 210.1 1.83366 0.0 213.81.83355 0.0 217.5 1.83361 0.0 221.4 1.83378 0.0 225.4 1.83400 0.0 229.61.83422 0.0 233.9 1.83439 0.0 238.4 1.83445 0.0 243.1 1.83434 0.0 248.01.83400 0.0 253.0 1.83326 0.0 258.3 1.83221 0.0 263.8 1.83083 0.0 269.51.82910 0.0 275.5 1.82700 0.0 281.8 1.82398 0.0 288.3 1.82067 0.0 295.21.81717 0.0 302.4 1.81358 0.0 310.0 1.81000 0.0 317.9 1.80699 0.0 326.31.80410 0.0 335.1 1.80130 0.0 344.4 1.79861 0.0 354.2 1.79600 0.0 364.71.79341 0.0 375.7 1.79090 0.0 387.5 1.78850 0.0 400.0 1.78619 0.0 413.31.78400 0.0 427.5 1.78202 0.0 442.8 1.78015 0.0 459.2 1.77837 0.0 476.91.77666 0.0 495.9 1.77500 0.0 516.6 1.77335 0.0 539.1 1.77174 0.0 563.61.77014 0.0 590.4 1.76857 0.0 619.9 1.76700 0.0 652.6 1.76540 0.0 688.81.76380 0.0 729.3 1.76220 0.0 774.9 1.76060 0.0 826.6 1.75900 0.0 885.61.75740 0.0 953.7 1.75580 0.0 1033.2 1.75420 0.0 1127.1 1.75260 0.01239.9 1.75100 0.0 1377.6 1.74900 0.0 1549.8 1.74600 0.0 1771.2 1.742000.0

TABLE 5 Refractive indices and dispersion curve for Nb₂O₅-RS vs.wavelength. Material Reactive sputtered Nb₂O₅ Wavelength (nm) RefractiveIndex (n) Extinction Coefficient (k) 206.6 2.04389 0.66079 250.0 2.329911.05691 300.2 3.14998 0.45732 325.0 2.94490 0.12012 350.2 2.747150.02027 375.1 2.62064 0.00048 400.6 2.53696 0.0 425.3 2.48169 0.0 450.02.44210 0.0 475.0 2.41223 0.0 500.9 2.38851 0.0 525.4 2.37086 0.0 549.82.35647 0.0 575.3 2.34409 0.0 600.4 2.33392 0.0 624.6 2.32557 0.0 650.82.31779 0.0 675.7 2.31142 0.0 700.5 2.30583 0.0 725.1 2.30093 0.0 749.12.29665 0.0 774.9 2.29255 0.0 799.9 2.28898 0.0 849.2 2.28288 0.0 901.72.27749 0.0 999.9 2.26958 0.0 1102.1 2.26342 0.0 1203.7 2.25867 0.01298.3 2.25513 0.0 1400.9 2.25198 0.0 1502.8 2.24939 0.0 1599.8 2.247300.0 1698.4 2.24547 0.0 1796.9 2.24389 0.0 1892.9 2.24254 0.0 1999.72.24122 0.0 2066.4 2.24047 0.0

TABLE 6 Refractive indices and dispersion curve for Al₂O3-RS vs.wavelength. Material Reactive sputtered Al₂O₃ Wavelength (nm) RefractiveIndex (n) Extinction Coefficient (k) 251.3 1.76256 0.0 275.2 1.74075 0.0300.8 1.72358 0.0 324.7 1.71136 0.0 350.2 1.70121 0.0 375.8 1.69321 0.0401.3 1.68679 0.0 425.2 1.68185 0.0 450.7 1.67747 0.0 474.7 1.67402 0.0500.2 1.67089 0.0 525.7 1.66823 0.0 549.5 1.66608 0.0 575.0 1.66408 0.0600.5 1.66234 0.0 625.9 1.66082 0.0 649.7 1.65955 0.0 675.1 1.65835 0.0700.5 1.65728 0.0 725.9 1.65633 0.0 749.7 1.65552 0.0 775.0 1.65474 0.0800.4 1.65404 0.0 850.9 1.65282 0.0 899.8 1.65184 0.0 950.2 1.65098 0.0999.0 1.65027 0.0 1100.0 1.64909 0.0 1199.6 1.64821 0.0 1302.0 1.647510.0 1400.8 1.64698 0.0 1499.7 1.64654 0.0 1599.0 1.64619 0.0 1688.41.64592 0.0

Anti-reflection coatings according to known designs and to embodimentsdescribed herein, low contrast structures were designed using therefractive index values thus obtained. As will be illustrated by theExamples, low-contrast anti-reflection coatings exhibit: 1) low contrastratios across a broad range of wavelength widths or across the visiblespectrum and for various surface defects, 2) low absolute reflectance R₂at areas with surface defects, and 3) low color shift at areas withsurface defects, at different incident illumination angles underdifferent illuminants, when compared to known anti-reflection coatings.In the Examples, color shifts were calculated relative to absolute white(0,0), using a D65 illuminant. The reflectance of the designs wasmodeled in an immersed state. As used herein, the phrase “immersedstate” includes the measurement of the average reflectance bysubtracting or otherwise removing reflections created by the article atinterfaces other than those involving the anti-reflection coating.Surface defect conditions used in the Examples are as follows: Condition“A”=surface thickness removal of 25 nm; Condition “B”=surface thicknessremoval of 50 nm; Condition “C”=surface thickness removal of 75 nm;Condition “D”=addition of contaminant having a thickness of 100 nm;Condition “E”=addition of contaminant having a thickness of 500 nm; andCondition “F”=addition of contaminant having a thickness of 2000 nm.

Modeled Comparative Examples 1 and 2

Modeled Examples 1 and 2 is an article having the same structure asshown in Tables 7 and 8. Modeled Example 1 includes a chemicallystrengthened alkali aluminoborosilicate glass substrate and ananti-reflection coating disposed on the substrate. Modeled Example 2includes a sapphire substrate and an anti-reflection coating disposed onthe substrate. The anti-reflection coating materials and thicknesses ofeach layer of material, in the order arranged in the anti-reflectioncoating, are provided in Tables 7 and 8.

TABLE 7 Structure of Modeled Comparative Example 1, in pristinecondition. Material Thickness (nm) Air Immersed SiO₂ 88.25 Nb₂O₅ 114.16 SiO₂ 35.24 Nb₂O₅ 12.41 ABS glass Immersed

TABLE 8 Structure of Modeled Comparative Example 2, in pristinecondition. Material Thickness (nm) Air Immersed SiO₂ 86 Nb₂O₅ 117.37SiO₂ 24.89 Nb₂O₅ 15.41 Sapphire Immersed

FIGS. 5A-5C illustrate the change in modeled reflectance, at normalincidence, of the coated surface of Modeled Comparative Examples 1 and 2in pristine condition and the coated surface of Modeled ComparativeExamples 1 and 2 with surface defect Conditions A, B and C. As shown inFIG. 5A, the reflectance of the coated surface of Modeled ComparativeExample 1 increases as the surface thickness removal increases.Specifically, the reflectance in the pristine condition is less thanabout 0.5% within the visible spectrum in the range from about 425 nm toabout 650 nm and the reflectance after surface defect Condition C isgreater than about 10.5% with 100 nm surface thickness removal withinthe same visible spectrum range, which is an increase of about 10%absolute reflectance. Thus, the visibility of the surface defectincreases, when compared to the rest of the anti-reflective coating,which is free of surface defects. FIG. 5B illustrates the contrast ratioof Modeled Comparative Example 1, after removal of different surfacethicknesses. The contrast ratios increase from significantly as largersurface thicknesses is removed and contrast ratio values of greater thanabout 15 and greater than about 45 are observed, over the visiblespectrum in the range from about 400 nm to about 700 nm. FIG. 5Cillustrates the contrast ratio of Modeled Comparative Example 2 andshows the surface defect visibility is even more pronounced (even at lowsurface thicknesses) when sapphire substrates are used.

FIG. 5D shows the modeled change in color in terms of Δa*b* fordifferent surface thickness removals and changing incident illuminationangle. At surface thickness removals in the range from about 30 nm toabout 70 nm, and from about 100 nm to 110 nm, Δa*b* values exceed 6 atincidence illumination angles up to about 60 degrees and can reach ashigh as 9, at incidence illumination angles of up to about 20 degrees.

Modeled Example 3

Modeled Example 3 is an article having a structure as shown in Table 9and includes a chemically strengthened ABS glass substrate and ananti-reflection coating disposed on the substrate. The anti-reflectioncoating materials and thicknesses of each layer of material, in theorder arranged in the anti-reflection coating, are provided in Table 9.

TABLE 9 Structure of Modeled Example 3, in pristine condition. MaterialThickness (nm) Air Immersed SiO₂ 108 AlO_(x)N_(y) 35 SiO₂ 38.8AlO_(x)N_(y) 34 SiO₂ 50.1 AlO_(x)N_(y) 11.5 ABS glass immersed

FIG. 6A illustrates the change in modeled reflectance at normalincidence of the coated surface of Modeled Example 3 in pristinecondition and with surface defect Conditions A, B and C. As shown in inFIG. 6A, the reflectance increases as the surface thickness removalincreases; however the increase in reflectance reduced, when compared toModeled Comparative Examples 1 and 2. In the pristine condition, thereflectance is about 1.2% within the visible spectrum in the range fromabout 400 nm to about 700 nm. The reflectance increases after surfacedefect Condition C (i.e., 100 nm surface thickness removal) to less thanabout 8% in the same visible spectrum range, which is an increase of6.8% absolute reflectance over the pristine condition. When compared toModeled Comparative Examples 1 and 2, the visibility of the surfacedefect including up to 100 nm surface thickness removal would besignificantly reduced. FIG. 6B illustrates the contrast ratio of theModeled Example 3, after removal of different surface thicknesses.Contrast ratio values of less than 6 are observed over the visiblespectrum in the range from about 400 nm to about 700 nm, even when up to100 nm of surface thickness was removed, which are significantly lessthan the contrast ratios observed with Modeled Comparative Examples 1and 2.

FIG. 6C shows the modeled change in color in terms of Δa*b* of thecoated surface of Modeled Example 3, after different surface thicknessremovals and changing incident illumination angle. The greatest changein color (or the highest values of Δa*b*) were observed at surfacethickness removals in the range from about 10 nm to about 20 m and fromabout 110 nm to about 130 nm, at which Δa*b* values are in the rangefrom about 4 to about 6, at incidence illumination angles of up to about60 degrees. At all other incident illumination angles and surfacethicknesses, the Δa*b* values are less than 4.

Modeled Example 4

Modeled Example 4 is an article having a structure as shown in Table 10and includes a sapphire substrate and an anti-reflection coatingdisposed on the substrate. The anti-reflection coating materials andthicknesses of each layer of material, in the order arranged in theanti-reflection coating, are provided in Table 10.

TABLE 10 Structure of Modeled Example 4, in pristine condition. MaterialThickness (nm) Air Immersed SiO₂ 120.6 AlO_(x)N_(y) 21.5 SiO₂ 42.8AlO_(x)N_(y) 29.6 SiO₂ 19.3 AlO_(x)N_(y) 6.2 Sapphire immersed

FIG. 7A illustrates the change in modeled reflectance at normalincidence of the coated surface of Modeled Example 4 in pristinecondition and with surface defect Conditions A, B and C. As shown in inFIG. 7A, the reflectance increases as the surface thickness removalincreases; however the increase in reflectance is reduced, when comparedto Modeled Comparative Examples 1 and 2. In the pristine condition, thereflectance was about 2.2% within the visible spectrum in the range fromabout 400 nm to about 700 nm. After surface defect Condition C (i.e.,removal of 100 nm of surface thickness), the reflectance increases toless than about 7% within the visible spectrum in the range from about400 nm to about 700 and to less than about 6% within the visiblespectrum in the range from about 420 nm to about 700 nm; and to lessthan about 5.5% within the visible spectrum in the range from about 450nm to about 700 nm. The increase in reflectance is less than about 4.8%absolute reflectance and, within some slightly narrower visible spectrumranges, less than about 3.3% absolute reflectance. When compared toModeled Comparative Examples 1 and 2, the visibility of a surface defectincluding up to 100 nm surface thickness removal would be significantlyreduced. FIG. 7B illustrates the contrast ratio of the Modeled Example4, after removal of different surface thicknesses. Contrast ratio valuesof less than 3 are observed over the visible spectrum in the range fromabout 400 nm to about 700 nm even when up to 100 nm of surface thicknesswas removed, which are significantly less than the contrast ratiosobserved with Modeled Comparative Examples 1 and 2.

FIG. 7C illustrates the modeled change in reflectance of the coatedsurface of Modeled Example 4 in pristine condition, at differentincident illumination angles. FIG. 7D shows the modeled change in colorin terms of Δa*b* for the coated surface of Modeled Example 4, afterdifferent surface thickness removals and changing incident illuminationangle. The greatest change in color (or the highest values of Δa*b*) areobserved at surface thickness removals in the range from about 10 nm to30 m, from about 60 nm to 130 nm and from about 120 nm to 135 nm, atwhich Δa*b* values are in the range from about 2.5 to about 4.5, atincident illumination angles of up to about 40 degrees. At all otherincident illumination angles and surface thicknesses, the Δa*b* valuesare less than 2.5.

Modeled Example 5

Modeled Example 5 is an article having a structure as shown in Table 11and includes a chemically strengthened ABS glass substrate and ananti-reflection coating disposed on the substrate. The anti-reflectioncoating materials and thicknesses of each layer of material, in theorder arranged in the anti-reflection coating, are provided in Table 11.

TABLE 11 Structure of Modeled Example 5, in pristine condition. MaterialThickness (nm) Air Immersed SiO₂ 99.18 AlO_(x)N_(y) 44.11 SiO₂ 8.26AlO_(x)N_(y) 86.41 SiO₂ 26.05 AlO_(x)N_(y) 26.64 SiO₂ 47.34 AlO_(x)N_(y)7.26 ABS glass immersed

FIG. 8A illustrates the change in modeled reflectance at normalincidence of the coated surface of Modeled Example 5 in pristinecondition and with surface defect Conditions A, B and C. As shown in inFIG. 8A, the reflectance increases as the surface thickness removalincreases; however the increase in reflectance is reduced, when comparedto Modeled Comparative Examples 1 and 2. In the pristine condition, thereflectance is about 1% within the visible spectrum in the range fromabout 450 nm to about 700 nm. After surface defect Condition C (i.e.,removal of 100 nm of surface thickness), the reflectance increases toless than about 8.5% within the visible spectrum in the range from about400 nm to about 700 and to less than about 7.5% within the visiblespectrum in the range from about 420 nm to about 700 nm. The increase inreflectance is less than about 7.5% absolute reflectance and in someslightly narrower visible spectrum ranges, less than about 6.5% absolutereflectance. When compared to Modeled Comparative Examples 1 and 2, thevisibility of the surface defect including up to 100 nm surfacethickness removal would be significantly reduced. FIG. 8B illustratesthe modeled contrast ratio of the Modeled Example 5, after removal ofdifferent surface thicknesses. Contrast ratio values of less than 9 areobserved over the visible spectrum in the range from about 400 nm toabout 700 nm, even when up to 100 nm of surface thickness is removed,which are significantly less than the contrast ratios observed withModeled Comparative Examples 1 and 2.

FIG. 8C illustrates the modeled change in reflectance of the coatedsurface of Modeled Example 5 in pristine condition, at differentincident illumination angles. FIG. 8D shows the modeled change in colorin terms of Δa*b* for the coated surface of Modeled Example 5, afterdifferent surface thickness removals and changing incident illuminationangle. The greatest change in color (or the highest values of Δa*b*) isobserved at surface thickness removals in the range from about 10 nm toabout 30 m, from about 60 nm to about 80 nm and from about 110 nm toabout 120 nm, at which Δa*b* values are in the range from about 3 toabout 4.5, at incident illumination angles of up to about 60 degrees. Atall other incident illumination angles and surface thicknesses, theΔa*b* values are less than 3.

Without being bound by theory, the thickness of one or more layers ofthe anti-reflection coating can be adjusted to impart a certain color orintentional deviation from flatness of the reflectance spectra. Forexample, Modeled Example 5 includes an intentional deviation fromflatness for the reflectance spectrum at normal incidence, which willimpart a slight blue coloration to the anti-reflection coating whenviewed in reflection at normal incidence. This can be a benefit in someapplications, for example, enabling 1) less variation in reflected colorcreated by manufacturing variations in layer thickness; and 2) arelatively flat reflectance spectrum at off angle-viewing, such as at 60degrees, as shown in FIGS. 8C and 8D.

In one or more embodiments, optical performance at greater incidentillumination angles (e.g. greater than about 60 degrees) may be improvedin some cases by adding additional layers to the anti-reflectioncoating, which enables the low-oscillation wavelength band to extendinto the near-IR wavelengths, such as to 800 nm, 900 nm, or even 1000nm, as shown in Modeled Example 5. This leads to lower oscillations andlower color at high incident illumination angles, because generally theentire reflectance spectrum of the article shifts to shorter wavelengthsat higher incident illumination angles.

Modeled Example 6

Modeled Example 6 is an article having a structure as shown in Table 12and includes a chemically strengthened ABS glass substrate and twoanti-reflection coatings. One anti-reflection coating includes ascratch-resistant layer (i.e., a 2000 nm-thick layer of AlO_(x)N_(y))and is disposed on the substrate. The second anti-reflection coating isdisposed on the first anti-reflection coating. The materials used forboth anti-reflection coatings and thicknesses of each layer of material,in the order arranged in the article, are provided in Table 12.

TABLE 12 Structure of Modeled Example 6, in pristine condition. MaterialThickness (nm) Air Immersed 1^(st) Anti- SiO₂ 104 reflectionAlO_(x)N_(y) 31.27 Coating SiO₂ 19.64 AlO_(x)N_(y) 56.25 SiO₂ 3.2 2^(nd)Anti- AlO_(x)N_(y) 2000 reflection SiO₂ 8.22 Coating AlO_(x)N_(y) 46.39SiO₂ 29 AlO_(x)N_(y) 27.87 SiO₂ 49.63 AlO_(x)N_(y) 9.34 ABS glassimmersed

FIG. 9A illustrates the change in modeled reflectance at normalincidence of the coated surface of Modeled Example 6 in pristinecondition and with surface defect Conditions A, B and C. As shown in inFIG. 9A, the reflectance increases as the surface thickness removalincreases; however the increase in reflectance is reduced, when comparedto Modeled Comparative Examples 1 and 2. In the pristine condition, thereflectance is in the range from about 1.5% to 2% within the visiblespectrum in the range from about 400 nm to about 700 nm. After surfacedefect Condition C (i.e., removal of 100 nm of surface thickness), thereflectance increases to less than about 7% within the same visiblespectrum range. The increase in reflectance is less than about 5.5%absolute reflectance. When compared to Modeled Comparative Examples 1and 2, the visibility of the surface defect including up to 100 nmsurface thickness removal would be significantly reduced. FIG. 9Billustrates the contrast ratio of the Modeled Example 6, after removalof different surface thicknesses. Contrast ratio values of less than 5are observed over the visible spectrum in the range from about 400 nm toabout 700 nm, even when up to 100 nm of surface thickness is removed,which are significantly less than the contrast ratios observed withModeled Comparative Examples 1 and 2.

FIG. 9C illustrates the modeled change in reflectance of the coatedsurface of Modeled Example 6 in pristine condition, at differentincident illumination angles. FIG. 9D illustrates the change inreflectance of the coated surface of Modeled Example 6 after surfacedefect Condition B, at different incident illumination angles. FIG. 9Eshows the contrast ratio of the coated surface shown in FIG. 9D. FIG. 9Fshows the change in color in terms of Δa*b* for different surfacethickness removals and changing incident illumination angle. Thegreatest change in color (or the highest values of Δa*b*) is observed atsurface thickness removals in the range from about 10 nm to about 30 m,from about 60 nm to about 80 nm and from about 110 nm to about 120 nm,at which Δa*b* values are in the range from about 2.5 to about 3.5, atincident illumination angles of up to about 60 degrees. At all otherincident illumination angles and surface thicknesses, the Δa*b* valuesare less than 2.5.

Modeled Comparative Example 7

Modeled Comparative Example 7 is an article having the structure asModeled Comparative Example 1. FIGS. 10A-10B illustrate the change inmodeled reflectance of a coated surface of Modeled Comparative Example 7in pristine condition and with a surface defect including Conditions D,E and F, with the contaminant being a fingerprint simulating medium.FIG. 10A shows the reflectance of the coated surface of ModeledComparative Example 7 in pristine condition and after the differentsurface defect Conditions. The reflectance increases as the thickness ofthe contaminant increases. Specifically, the reflectance in the pristinecondition is less than about 0.5% within the visible spectrum in therange from about 425 nm to about 650 nm. The reflectance after surfacedefect Condition D is greater than about 9% within the same visiblespectrum range, and the reflectance after surface defect Conditions Eand F includes oscillations with amplitudes as great as about 12%absolute reflectance, with reflectance maximums of greater than about12%, over narrower ranges of the visible spectrum. The increase inreflectance between the pristine condition and surface defects D-F wasmodeled as about 11.5% or greater absolute reflectance. Thus, thevisibility of the surface defect increases significantly, when comparedto the remainder of the anti-reflective coating, which is free ofsurface defects. FIG. 10B illustrates the contrast ratio of the modeledstructure shown in FIG. 10A, for each of surface defect Conditions D-F.The contrast ratio spectra oscillate significantly and exceed 100 forConditions D and E, over the visible spectrum in the range from about400 nm to about 700 nm.

Modeled Example 8

Modeled Example 8 included an article having the same structure asModeled Example 3.

FIG. 11A illustrates the change in modeled reflectance at normalincidence of the coated surface of Modeled Example 8 in pristinecondition and with surface defect Conditions D, E and F. As shown inFIG. 11A, the reflectance increases as the surface thickness removalincreases; however the increase in reflectance is reduced, when comparedto Modeled Comparative Example 7. In pristine condition, the reflectanceis about 1.2% within the visible spectrum in the range from about 400 nmto about 700 nm. After surface defect Condition D, the reflectanceincreases to less than about 8% within the visible spectrum range fromabout 400 nm to about 700 nm. After surface defect Condition E, thereflectance increases to less than about 8% within the visible spectrumrange from about 450 nm to about 700 nm. After surface defect ConditionF, the reflectance increases to less than about 8.5% within the visiblespectrum range from about 425 nm to about 675 nm. The increase inreflectance is less than about 7.3% absolute reflectance. When comparedto Modeled Comparative Example 7, the visibility of surface defectsincluding the addition of up to 2000 nm of fingerprint simulating mediumwould be significantly reduced. FIG. 11B illustrates the contrast ratioof the Modeled Example 8, after the addition of different thicknesses offingerprint simulating medium. Contrast ratio values of less than 7.5are observed over the visible spectrum in the range from about 400 nm toabout 700 nm, even when fingerprint simulating medium having a thicknessup to 2000 nm is present on the coated surface, which are significantlyless than the contrast ratios observed with Modeled Comparative Example7.

Modeled Example 9

Modeled Example 9 included an article having the same structure asModeled Example 4.

FIG. 12A illustrates the change in modeled reflectance at normalincidence of the coated surface of Modeled Example 9 in pristinecondition and with surface defect Conditions D, E and F, at normalincidence. As shown in FIG. 12A, the reflectance increases as thesurface thickness removal increases; however the increase in reflectancewas reduced, when compared to Modeled Comparative Example 7. In thepristine condition, the reflectance is about 2.2% within the visiblespectrum in the range from about 400 nm to about 700 nm. After surfacedefect Condition D, the reflectance increases to less than about 6%within the visible spectrum range from about 400 nm to about 700 nm.After surface defect Condition E, the reflectance increases to less thanabout 6% within the visible spectrum range from about 450 nm to about700 nm. After surface defect Condition F, the reflectance increases toless than about 6% within the visible spectrum range from about 450 nmto about 700 nm. The increase in reflectance is less than about 3.8%absolute reflectance. When compared to Modeled Comparative Example 7,the visibility of surface defects including the addition of up to 2000nm of fingerprint simulating medium would be significantly reduced. FIG.12B illustrates the contrast ratio of the Modeled Example 9, after theaddition of different thicknesses of the fingerprint simulating medium.Contrast ratio values of less than 3.3 are observed over the visiblespectrum in the range from about 400 nm to about 700 nm, even whenfingerprint simulating medium having a thickness up to 2000 nm ispresent on the coated surface, which are significantly less than thecontrast ratios observed with Modeled Comparative Example 7.

Modeled Example 10

Modeled Example 10 includes an article having the same structure asModeled Example 6. FIG. 13A illustrates the change in modeledreflectance at normal incidence of the coated surface of Modeled Example10 in pristine condition and with surface defect Conditions D, E and F.As shown in in FIG. 13A, the reflectance increases as the thickness ofthe contaminant increases; however the increase in reflectance wasreduced, when compared to Modeled Comparative Example 7. In the pristinecondition, the reflectance is in the range from about 1.5% to 2% withinthe visible spectrum in the range from about 400 nm to about 700 nm.After surface defect Condition D and E, the reflectance increases toless than about 7.5% within the same visible spectrum range. Aftersurface defect Condition F, the reflectance increases to less than about8% within the same visible spectrum range. The increase in reflectanceis less than about 6.5% absolute reflectance. When compared to ModeledComparative Example 7 1 and 2, the visibility of the surface defectincluding a fingerprint simulating medium contaminant having a thicknessup to about 200 nm would be significantly reduced. FIG. 13B illustratesthe contrast ratio of the Modeled Example 10, after removal of differentsurface thicknesses. Contrast ratio values of less than 5.5 are observedover the visible spectrum in the range from about 400 nm to about 700nm, even when fingerprint simulating medium having a thickness up to2000 nm is present on the coated surface, which are significantly lessthan the contrast ratios observed with Modeled Comparative Example 7.

Modeled Examples 11 and 12

Examples 11-12 used modeling to understand the reflectance spectra ofarticles in which the anti-reflection coating is pristine and includes asurface defect. The modeling was based on collected refractive indexdata from formed layers of various materials that may be used in theanti-reflection coatings and a substrate of ABS glass. The layers of theanti-reflection coating were formed by vacuum deposition. Some of theformed layers included SiO₂, and AlOxNy formed at different thicknesses(e.g.. 100 nm and 2000 nm). The refractive indices (as a function ofwavelength) of the formed layers of the optical film and the substrateswere measured using spectroscopic ellipsometry. Tables 13-15 include therefractive indices and dispersion curves measured. The refractiveindices thus measured were then used to calculate reflectance spectrafor the Modeled Examples 11 and 12.

TABLE 13 Refractive indices and dispersion curve for a SiO₂ layer vs.wavelength. Wavelength Refractive Index Extinction Coefficient 3501.49325 0.00006 351 1.49311 0.00006 352 1.49297 0.00006 353 1.492830.00006 354 1.4927 0.00006 355 1.49256 0.00007 356 1.49243 0.00007 3571.49229 0.00007 358 1.49216 0.00007 359 1.49202 0.00007 360 1.491890.00007 361 1.49176 0.00007 362 1.49163 0.00007 363 1.4915 0.00007 3641.49137 0.00007 365 1.49124 0.00007 366 1.49112 0.00007 367 1.490990.00007 368 1.49086 0.00007 369 1.49074 0.00007 370 1.49061 0.00007 3711.49049 0.00007 372 1.49037 0.00007 373 1.49024 0.00007 374 1.490120.00007 375 1.49 0.00007 376 1.48988 0.00007 377 1.48976 0.00007 3781.48964 0.00007 379 1.48952 0.00007 380 1.48941 0.00007 381 1.489290.00007 382 1.48917 0.00007 383 1.48906 0.00007 384 1.48894 0.00007 3851.48883 0.00007 386 1.48872 0.00007 387 1.4886 0.00007 388 1.488490.00007 389 1.48838 0.00007 390 1.48827 0.00007 391 1.48816 0.00007 3921.48805 0.00007 393 1.48794 0.00007 394 1.48783 0.00007 395 1.487720.00007 396 1.48762 0.00007 397 1.48751 0.00007 398 1.4874 0.00007 3991.4873 0.00007 400 1.48719 0.00007 401 1.48709 0.00007 402 1.486980.00007 403 1.48688 0.00007 404 1.48678 0.00007 405 1.48668 0.00007 4061.48658 0.00007 407 1.48647 0.00007 408 1.48637 0.00007 409 1.486270.00007 410 1.48618 0.00007 411 1.48608 0.00007 412 1.48598 0.00007 4131.48588 0.00007 414 1.48578 0.00007 415 1.48569 0.00007 416 1.485590.00007 417 1.4855 0.00007 418 1.4854 0.00007 419 1.48531 0.00007 4201.48521 0.00007 421 1.48512 0.00007 422 1.48503 0.00007 423 1.484940.00007 424 1.48484 0.00007 425 1.48475 0.00007 426 1.48466 0.00007 4271.48457 0.00007 428 1.48448 0.00007 429 1.48439 0.00007 430 1.48430.00007 431 1.48422 0.00007 432 1.48413 0.00007 433 1.48404 0.00007 4341.48395 0.00007 435 1.48387 0.00007 436 1.48378 0.00007 437 1.48370.00007 438 1.48361 0.00007 439 1.48353 0.00007 440 1.48344 0.00007 4411.48336 0.00007 442 1.48328 0.00007 443 1.48319 0.00007 444 1.483110.00007 445 1.48303 0.00007 446 1.48295 0.00007 447 1.48287 0.00007 4481.48279 0.00007 449 1.48271 0.00007 450 1.48263 0.00007 451 1.482550.00007 452 1.48247 0.00007 453 1.48239 0.00007 454 1.48231 0.00007 4551.48223 0.00007 456 1.48216 0.00007 457 1.48208 0.00007 458 1.4820.00007 459 1.48193 0.00007 460 1.48185 0.00007 461 1.48178 0.00007 4621.4817 0.00007 463 1.48163 0.00007 464 1.48155 0.00007 465 1.481480.00007 466 1.48141 0.00007 467 1.48133 0.00007 468 1.48126 0.00007 4691.48119 0.00007 470 1.48112 0.00007 471 1.48104 0.00007 472 1.480970.00007 473 1.4809 0.00007 474 1.48083 0.00007 475 1.48076 0.00007 4761.48069 0.00007 477 1.48062 0.00007 478 1.48056 0.00006 479 1.480490.00006 480 1.48042 0.00006 481 1.48035 0.00006 482 1.48028 0.00006 4831.48022 0.00006 484 1.48015 0.00006 485 1.48008 0.00006 486 1.480020.00006 487 1.47995 0.00006 488 1.47989 0.00006 489 1.47982 0.00006 4901.47976 0.00006 491 1.47969 0.00006 492 1.47963 0.00006 493 1.479560.00006 494 1.4795 0.00006 495 1.47944 0.00006 496 1.47937 0.00006 4971.47931 0.00006 498 1.47925 0.00006 499 1.47919 0.00006 500 1.479130.00006 501 1.47906 0.00006 502 1.479 0.00006 503 1.47894 0.00006 5041.47888 0.00006 505 1.47882 0.00006 506 1.47876 0.00006 507 1.47870.00006 508 1.47864 0.00006 509 1.47858 0.00006 510 1.47853 0.00006 5111.47847 0.00006 512 1.47841 0.00006 513 1.47835 0.00006 514 1.478290.00006 515 1.47824 0.00006 516 1.47818 0.00005 517 1.47812 0.00005 5181.47807 0.00005 519 1.47801 0.00005 520 1.47795 0.00005 521 1.47790.00005 522 1.47784 0.00005 523 1.47779 0.00005 524 1.47773 0.00005 5251.47768 0.00005 526 1.47763 0.00005 527 1.47757 0.00005 528 1.477520.00005 529 1.47746 0.00005 530 1.47741 0.00005 531 1.47736 0.00005 5321.47731 0.00005 533 1.47725 0.00005 534 1.4772 0.00005 535 1.477150.00005 536 1.4771 0.00005 537 1.47705 0.00005 538 1.47699 0.00005 5391.47694 0.00005 540 1.47689 0.00005 541 1.47684 0.00005 542 1.476790.00005 543 1.47674 0.00005 544 1.47669 0.00005 545 1.47664 0.00005 5461.47659 0.00005 547 1.47654 0.00005 548 1.47649 0.00005 549 1.476450.00005 550 1.4764 0.00005 551 1.47635 0.00005 552 1.4763 0.00004 5531.47625 0.00004 554 1.47621 0.00004 555 1.47616 0.00004 556 1.476110.00004 557 1.47607 0.00004 558 1.47602 0.00004 559 1.47597 0.00004 5601.47593 0.00004 561 1.47588 0.00004 562 1.47583 0.00004 563 1.475790.00004 564 1.47574 0.00004 565 1.4757 0.00004 566 1.47565 0.00004 5671.47561 0.00004 568 1.47556 0.00004 569 1.47552 0.00004 570 1.475480.00004 571 1.47543 0.00004 572 1.47539 0.00004 573 1.47534 0.00004 5741.4753 0.00004 575 1.47526 0.00004 576 1.47521 0.00004 577 1.475170.00004 578 1.47513 0.00004 579 1.47509 0.00004 580 1.47504 0.00004 5811.475 0.00004 582 1.47496 0.00004 583 1.47492 0.00004 584 1.474880.00004 585 1.47484 0.00004 586 1.4748 0.00004 587 1.47475 0.00004 5881.47471 0.00004 589 1.47467 0.00003 590 1.47463 0.00003 591 1.474590.00003 592 1.47455 0.00003 593 1.47451 0.00003 594 1.47447 0.00003 5951.47443 0.00003 596 1.47439 0.00003 597 1.47436 0.00003 598 1.474320.00003 599 1.47428 0.00003 600 1.47424 0.00003 601 1.4742 0.00003 6021.47416 0.00003 603 1.47412 0.00003 604 1.47409 0.00003 605 1.474050.00003 606 1.47401 0.00003 607 1.47397 0.00003 608 1.47394 0.00003 6091.4739 0.00003 610 1.47386 0.00003 611 1.47383 0.00003 612 1.473790.00003 613 1.47375 0.00003 614 1.47372 0.00003 615 1.47368 0.00003 6161.47364 0.00003 617 1.47361 0.00003 618 1.47357 0.00003 619 1.473540.00003 620 1.4735 0.00003 621 1.47347 0.00003 622 1.47343 0.00003 6231.4734 0.00003 624 1.47336 0.00003 625 1.47333 0.00003 626 1.473290.00003 627 1.47326 0.00003 628 1.47322 0.00003 629 1.47319 0.00003 6301.47316 0.00003 631 1.47312 0.00003 632 1.47309 0.00003 633 1.473050.00002 634 1.47302 0.00002 635 1.47299 0.00002 636 1.47296 0.00002 6371.47292 0.00002 638 1.47289 0.00002 639 1.47286 0.00002 640 1.472820.00002 641 1.47279 0.00002 642 1.47276 0.00002 643 1.47273 0.00002 6441.4727 0.00002 645 1.47266 0.00002 646 1.47263 0.00002 647 1.47260.00002 648 1.47257 0.00002 649 1.47254 0.00002 650 1.47251 0.00002 6511.47248 0.00002 652 1.47244 0.00002 653 1.47241 0.00002 654 1.472380.00002 655 1.47235 0.00002 656 1.47232 0.00002 657 1.47229 0.00002 6581.47226 0.00002 659 1.47223 0.00002 660 1.4722 0.00002 661 1.472170.00002 662 1.47214 0.00002 663 1.47211 0.00002 664 1.47208 0.00002 6651.47205 0.00002 666 1.47202 0.00002 667 1.472 0.00002 668 1.471970.00002 669 1.47194 0.00002 670 1.47191 0.00002 671 1.47188 0.00002 6721.47185 0.00002 673 1.47182 0.00002 674 1.47179 0.00002 675 1.471770.00002 676 1.47174 0.00002 677 1.47171 0.00002 678 1.47168 0.00002 6791.47166 0.00002 680 1.47163 0.00002 681 1.4716 0.00002 682 1.471570.00002 683 1.47155 0.00002 684 1.47152 0.00002 685 1.47149 0.00002 6861.47146 0.00002 687 1.47144 0.00002 688 1.47141 0.00002 689 1.471380.00002 690 1.47136 0.00002 691 1.47133 0.00002 692 1.4713 0.00002 6931.47128 0.00001 694 1.47125 0.00001 695 1.47123 0.00001 696 1.47120.00001 697 1.47117 0.00001 698 1.47115 0.00001 699 1.47112 0.00001 7001.4711 0.00001 701 1.47107 0.00001 702 1.47105 0.00001 703 1.471020.00001 704 1.471 0.00001 705 1.47097 0.00001 706 1.47095 0.00001 7071.47092 0.00001 708 1.4709 0.00001 709 1.47087 0.00001 710 1.470850.00001 711 1.47082 0.00001 712 1.4708 0.00001 713 1.47077 0.00001 7141.47075 0.00001 715 1.47073 0.00001 716 1.4707 0.00001 717 1.470680.00001 718 1.47065 0.00001 719 1.47063 0.00001 720 1.47061 0.00001 7211.47058 0.00001 722 1.47056 0.00001 723 1.47054 0.00001 724 1.470510.00001 725 1.47049 0.00001 726 1.47047 0.00001 727 1.47044 0.00001 7281.47042 0.00001 729 1.4704 0.00001 730 1.47038 0.00001 731 1.470350.00001 732 1.47033 0.00001 733 1.47031 0.00001 734 1.47029 0.00001 7351.47026 0.00001 736 1.47024 0.00001 737 1.47022 0.00001 738 1.47020.00001 739 1.47017 0.00001 740 1.47015 0.00001 741 1.47013 0.00001 7421.47011 0.00001 743 1.47009 0.00001 744 1.47007 0.00001 745 1.470040.00001 746 1.47002 0.00001 747 1.47 0.00001 748 1.46998 0.00001 7491.46996 0.00001 750 1.46994 0.00001 751 1.46992 0.00001 752 1.46990.00001 753 1.46987 0.00001 754 1.46985 0.00001 755 1.46983 0.00001 7561.46981 0.00001 757 1.46979 0.00001 758 1.46977 0.00001 759 1.469750.00001 760 1.46973 0.00001 761 1.46971 0.00001 762 1.46969 0.00001 7631.46967 0.00001 764 1.46965 0.00001 765 1.46963 0.00001 766 1.469610.00001 767 1.46959 0.00001 768 1.46957 0.00001 769 1.46955 0.00001 7701.46953 0.00001 771 1.46951 0.00001 772 1.46949 0.00001 773 1.469470.00001 774 1.46945 0.00001 775 1.46943 0.00001 776 1.46941 0.00001 7771.46939 0.00001 778 1.46938 0.00001 779 1.46936 0.00001 780 1.469340.00001 781 1.46932 0.00001 782 1.4693 0.00001 783 1.46928 0.00001 7841.46926 0.00001 785 1.46924 0.00001 786 1.46923 0.00001 787 1.469210.00001 788 1.46919 0.00001 789 1.46917 0.00001 790 1.46915 0.00001 7911.46913 0.00001 792 1.46912 0.00001 793 1.4691 0.00001 794 1.469080.00001 795 1.46906 0.00001 796 1.46904 0.00001 797 1.46903 0.00001 7981.46901 0.00001

TABLE 14 Refractive indices and dispersion curve for a AlOxNy layerhaving a thickness of 100 nm vs. wavelength. Wavelength Refractive IndexExtinction Coefficient 350 2.05658 0 351 2.05585 0 352 2.05512 0 3532.0544 0 354 2.05369 0 355 2.05299 0 356 2.05229 0 357 2.0516 0 3582.05091 0 359 2.05023 0 360 2.04955 0 361 2.04888 0 362 2.04822 0 3632.04756 0 364 2.04691 0 365 2.04626 0 366 2.04562 0 367 2.04498 0 3682.04435 0 369 2.04372 0 370 2.0431 0 371 2.04249 0 372 2.04188 0 3732.04127 0 374 2.04067 0 375 2.04007 0 376 2.03948 0 377 2.0389 0 3782.03832 0 379 2.03774 0 380 2.03717 0 381 2.0366 0 382 2.03604 0 3832.03548 0 384 2.03492 0 385 2.03437 0 386 2.03383 0 387 2.03329 0 3882.03275 0 389 2.03222 0 390 2.03169 0 391 2.03117 0 392 2.03065 0 3932.03013 0 394 2.02962 0 395 2.02911 0 396 2.02861 0 397 2.02811 0 3982.02761 0 399 2.02712 0 400 2.02663 0 401 2.02614 0 402 2.02566 0 4032.02518 0 404 2.02471 0 405 2.02424 0 406 2.02377 0 407 2.02331 0 4082.02285 0 409 2.02239 0 410 2.02194 0 411 2.02149 0 412 2.02104 0 4132.0206 0 414 2.02016 0 415 2.01972 0 416 2.01929 0 417 2.01886 0 4182.01843 0 419 2.01801 0 420 2.01759 0 421 2.01717 0 422 2.01675 0 4232.01634 0 424 2.01593 0 425 2.01553 0 426 2.01512 0 427 2.01472 0 4282.01433 0 429 2.01393 0 430 2.01354 0 431 2.01315 0 432 2.01276 0 4332.01238 0 434 2.012 0 435 2.01162 0 436 2.01125 0 437 2.01087 0 4382.0105 0 439 2.01014 0 440 2.00977 0 441 2.00941 0 442 2.00905 0 4432.00869 0 444 2.00833 0 445 2.00798 0 446 2.00763 0 447 2.00728 0 4482.00694 0 449 2.00659 0 450 2.00625 0 451 2.00591 0 452 2.00558 0 4532.00524 0 454 2.00491 0 455 2.00458 0 456 2.00425 0 457 2.00393 0 4582.00361 0 459 2.00328 0 460 2.00297 0 461 2.00265 0 462 2.00233 0 4632.00202 0 464 2.00171 0 465 2.0014 0 466 2.0011 0 467 2.00079 0 4682.00049 0 469 2.00019 0 470 1.99989 0 471 1.99959 0 472 1.9993 0 4731.999 0 474 1.99871 0 475 1.99842 0 476 1.99814 0 477 1.99785 0 4781.99757 0 479 1.99729 0 480 1.99701 0 481 1.99673 0 482 1.99645 0 4831.99618 0 484 1.9959 0 485 1.99563 0 486 1.99536 0 487 1.99509 0 4881.99483 0 489 1.99456 0 490 1.9943 0 491 1.99404 0 492 1.99378 0 4931.99352 0 494 1.99326 0 495 1.99301 0 496 1.99275 0 497 1.9925 0 4981.99225 0 499 1.992 0 500 1.99175 0 501 1.99151 0 502 1.99126 0 5031.99102 0 504 1.99078 0 505 1.99054 0 506 1.9903 0 507 1.99006 0 5081.98983 0 509 1.98959 0 510 1.98936 0 511 1.98913 0 512 1.9889 0 5131.98867 0 514 1.98844 0 515 1.98822 0 516 1.98799 0 517 1.98777 0 5181.98755 0 519 1.98733 0 520 1.98711 0 521 1.98689 0 522 1.98667 0 5231.98645 0 524 1.98624 0 525 1.98603 0 526 1.98581 0 527 1.9856 0 5281.98539 0 529 1.98519 0 530 1.98498 0 531 1.98477 0 532 1.98457 0 5331.98436 0 534 1.98416 0 535 1.98396 0 536 1.98376 0 537 1.98356 0 5381.98336 0 539 1.98317 0 540 1.98297 0 541 1.98277 0 542 1.98258 0 5431.98239 0 544 1.9822 0 545 1.98201 0 546 1.98182 0 547 1.98163 0 5481.98144 0 549 1.98126 0 550 1.98107 0 551 1.98089 0 552 1.9807 0 5531.98052 0 554 1.98034 0 555 1.98016 0 556 1.97998 0 557 1.9798 0 5581.97962 0 559 1.97945 0 560 1.97927 0 561 1.9791 0 562 1.97892 0 5631.97875 0 564 1.97858 0 565 1.97841 0 566 1.97824 0 567 1.97807 0 5681.9779 0 569 1.97774 0 570 1.97757 0 571 1.9774 0 572 1.97724 0 5731.97708 0 574 1.97691 0 575 1.97675 0 576 1.97659 0 577 1.97643 0 5781.97627 0 579 1.97611 0 580 1.97596 0 581 1.9758 0 582 1.97564 0 5831.97549 0 584 1.97533 0 585 1.97518 0 586 1.97503 0 587 1.97487 0 5881.97472 0 589 1.97457 0 590 1.97442 0 591 1.97427 0 592 1.97413 0 5931.97398 0 594 1.97383 0 595 1.97369 0 596 1.97354 0 597 1.9734 0 5981.97325 0 599 1.97311 0 600 1.97297 0 601 1.97283 0 602 1.97268 0 6031.97254 0 604 1.9724 0 605 1.97227 0 606 1.97213 0 607 1.97199 0 6081.97185 0 609 1.97172 0 610 1.97158 0 611 1.97145 0 612 1.97131 0 6131.97118 0 614 1.97105 0 615 1.97092 0 616 1.97078 0 617 1.97065 0 6181.97052 0 619 1.97039 0 620 1.97027 0 621 1.97014 0 622 1.97001 0 6231.96988 0 624 1.96976 0 625 1.96963 0 626 1.96951 0 627 1.96938 0 6281.96926 0 629 1.96913 0 630 1.96901 0 631 1.96889 0 632 1.96877 0 6331.96865 0 634 1.96853 0 635 1.96841 0 636 1.96829 0 637 1.96817 0 6381.96805 0 639 1.96793 0 640 1.96782 0 641 1.9677 0 642 1.96758 0 6431.96747 0 644 1.96735 0 645 1.96724 0 646 1.96712 0 647 1.96701 0 6481.9669 0 649 1.96679 0 650 1.96668 0 651 1.96656 0 652 1.96645 0 6531.96634 0 654 1.96623 0 655 1.96612 0 656 1.96602 0 657 1.96591 0 6581.9658 0 659 1.96569 0 660 1.96559 0 661 1.96548 0 662 1.96537 0 6631.96527 0 664 1.96516 0 665 1.96506 0 666 1.96496 0 667 1.96485 0 6681.96475 0 669 1.96465 0 670 1.96455 0 671 1.96445 0 672 1.96434 0 6731.96424 0 674 1.96414 0 675 1.96404 0 676 1.96394 0 677 1.96385 0 6781.96375 0 679 1.96365 0 680 1.96355 0 681 1.96346 0 682 1.96336 0 6831.96326 0 684 1.96317 0 685 1.96307 0 686 1.96298 0 687 1.96288 0 6881.96279 0 689 1.96269 0 690 1.9626 0 691 1.96251 0 692 1.96242 0 6931.96232 0 694 1.96223 0 695 1.96214 0 696 1.96205 0 697 1.96196 0 6981.96187 0 699 1.96178 0 700 1.96169 0 701 1.9616 0 702 1.96151 0 7031.96143 0 704 1.96134 0 705 1.96125 0 706 1.96116 0 707 1.96108 0 7081.96099 0 709 1.96091 0 710 1.96082 0 711 1.96073 0 712 1.96065 0 7131.96057 0 714 1.96048 0 715 1.9604 0 716 1.96031 0 717 1.96023 0 7181.96015 0 719 1.96007 0 720 1.95998 0 721 1.9599 0 722 1.95982 0 7231.95974 0 724 1.95966 0 725 1.95958 0 726 1.9595 0 727 1.95942 0 7281.95934 0 729 1.95926 0 730 1.95918 0 731 1.95911 0 732 1.95903 0 7331.95895 0 734 1.95887 0 735 1.9588 0 736 1.95872 0 737 1.95864 0 7381.95857 0 739 1.95849 0 740 1.95841 0 741 1.95834 0 742 1.95826 0 7431.95819 0 744 1.95812 0 745 1.95804 0 746 1.95797 0 747 1.9579 0 7481.95782 0 749 1.95775 0 750 1.95768 0 751 1.9576 0 752 1.95753 0 7531.95746 0 754 1.95739 0 755 1.95732 0 756 1.95725 0 757 1.95718 0 7581.95711 0 759 1.95704 0 760 1.95697 0 761 1.9569 0 762 1.95683 0 7631.95676 0 764 1.95669 0 765 1.95662 0 766 1.95656 0 767 1.95649 0 7681.95642 0 769 1.95635 0 770 1.95629 0 771 1.95622 0 772 1.95615 0 7731.95609 0 774 1.95602 0 775 1.95596 0 776 1.95589 0 777 1.95583 0 7781.95576 0 779 1.9557 0 780 1.95563 0 781 1.95557 0 782 1.9555 0 7831.95544 0 784 1.95538 0 785 1.95531 0 786 1.95525 0 787 1.95519 0 7881.95513 0 789 1.95506 0 790 1.955 0 791 1.95494 0 792 1.95488 0 7931.95482 0 794 1.95476 0 795 1.9547 0 796 1.95463 0 797 1.95457 0 7981.95451 0

TABLE 15 Refractive indices and dispersion curve for a AlOxNy layerhaving a thickness of 2000 nm vs. wavelength. Wavelength RefractiveIndex Extinction Coefficient 350 2.03915 0.00065 351 2.03836 0.00064 3522.03758 0.00064 353 2.03681 0.00063 354 2.03605 0.00063 355 2.035290.00062 356 2.03454 0.00062 357 2.0338 0.00061 358 2.03307 0.00061 3592.03234 0.0006 360 2.03162 0.0006 361 2.03091 0.00059 362 2.030210.00059 363 2.02951 0.00059 364 2.02882 0.00058 365 2.02813 0.00058 3662.02746 0.00057 367 2.02678 0.00057 368 2.02612 0.00056 369 2.025460.00056 370 2.02481 0.00055 371 2.02416 0.00055 372 2.02352 0.00055 3732.02289 0.00054 374 2.02226 0.00054 375 2.02164 0.00053 376 2.021020.00053 377 2.02041 0.00053 378 2.01981 0.00052 379 2.01921 0.00052 3802.01862 0.00051 381 2.01803 0.00051 382 2.01744 0.00051 383 2.016870.0005 384 2.0163 0.0005 385 2.01573 0.0005 386 2.01517 0.00049 3872.01461 0.00049 388 2.01406 0.00048 389 2.01351 0.00048 390 2.012970.00048 391 2.01243 0.00047 392 2.0119 0.00047 393 2.01137 0.00047 3942.01085 0.00046 395 2.01033 0.00046 396 2.00982 0.00046 397 2.009310.00045 398 2.00881 0.00045 399 2.00831 0.00045 400 2.00781 0.00044 4012.00732 0.00044 402 2.00683 0.00043 403 2.00635 0.00043 404 2.005870.00043 405 2.00539 0.00043 406 2.00492 0.00042 407 2.00446 0.00042 4082.00399 0.00042 409 2.00353 0.00041 410 2.00308 0.00041 411 2.002630.00041 412 2.00218 0.0004 413 2.00174 0.0004 414 2.0013 0.0004 4152.00086 0.00039 416 2.00043 0.00039 417 2 0.00039 418 1.99957 0.00039419 1.99915 0.00038 420 1.99873 0.00038 421 1.99832 0.00038 422 1.997910.00037 423 1.9975 0.00037 424 1.99709 0.00037 425 1.99669 0.00037 4261.99629 0.00036 427 1.9959 0.00036 428 1.9955 0.00036 429 1.995110.00035 430 1.99473 0.00035 431 1.99435 0.00035 432 1.99397 0.00035 4331.99359 0.00034 434 1.99321 0.00034 435 1.99284 0.00034 436 1.992480.00034 437 1.99211 0.00033 438 1.99175 0.00033 439 1.99139 0.00033 4401.99103 0.00033 441 1.99068 0.00032 442 1.99033 0.00032 443 1.989980.00032 444 1.98963 0.00032 445 1.98929 0.00031 446 1.98895 0.00031 4471.98861 0.00031 448 1.98827 0.00031 449 1.98794 0.0003 450 1.987610.0003 451 1.98728 0.0003 452 1.98696 0.0003 453 1.98663 0.00029 4541.98631 0.00029 455 1.986 0.00029 456 1.98568 0.00029 457 1.985370.00029 458 1.98506 0.00028 459 1.98475 0.00028 460 1.98444 0.00028 4611.98414 0.00028 462 1.98383 0.00028 463 1.98353 0.00027 464 1.983240.00027 465 1.98294 0.00027 466 1.98265 0.00027 467 1.98235 0.00027 4681.98207 0.00026 469 1.98178 0.00026 470 1.98149 0.00026 471 1.981210.00026 472 1.98093 0.00026 473 1.98065 0.00025 474 1.98037 0.00025 4751.9801 0.00025 476 1.97982 0.00025 477 1.97955 0.00025 478 1.979280.00024 479 1.97902 0.00024 480 1.97875 0.00024 481 1.97849 0.00024 4821.97823 0.00024 483 1.97797 0.00023 484 1.97771 0.00023 485 1.977450.00023 486 1.9772 0.00023 487 1.97694 0.00023 488 1.97669 0.00023 4891.97644 0.00022 490 1.97619 0.00022 491 1.97595 0.00022 492 1.97570.00022 493 1.97546 0.00022 494 1.97522 0.00022 495 1.97498 0.00021 4961.97474 0.00021 497 1.97451 0.00021 498 1.97427 0.00021 499 1.974040.00021 500 1.97381 0.00021 501 1.97358 0.0002 502 1.97335 0.0002 5031.97312 0.0002 504 1.9729 0.0002 505 1.97267 0.0002 506 1.97245 0.0002507 1.97223 0.0002 508 1.97201 0.00019 509 1.97179 0.00019 510 1.971570.00019 511 1.97136 0.00019 512 1.97114 0.00019 513 1.97093 0.00019 5141.97072 0.00019 515 1.97051 0.00018 516 1.9703 0.00018 517 1.970090.00018 518 1.96989 0.00018 519 1.96968 0.00018 520 1.96948 0.00018 5211.96928 0.00018 522 1.96908 0.00017 523 1.96888 0.00017 524 1.968680.00017 525 1.96848 0.00017 526 1.96829 0.00017 527 1.96809 0.00017 5281.9679 0.00017 529 1.96771 0.00017 530 1.96752 0.00016 531 1.967330.00016 532 1.96714 0.00016 533 1.96695 0.00016 534 1.96677 0.00016 5351.96658 0.00016 536 1.9664 0.00016 537 1.96621 0.00016 538 1.966030.00015 539 1.96585 0.00015 540 1.96567 0.00015 541 1.96549 0.00015 5421.96532 0.00015 543 1.96514 0.00015 544 1.96497 0.00015 545 1.964790.00015 546 1.96462 0.00015 547 1.96445 0.00014 548 1.96428 0.00014 5491.96411 0.00014 550 1.96394 0.00014 551 1.96377 0.00014 552 1.96360.00014 553 1.96344 0.00014 554 1.96327 0.00014 555 1.96311 0.00014 5561.96295 0.00013 557 1.96278 0.00013 558 1.96262 0.00013 559 1.962460.00013 560 1.9623 0.00013 561 1.96215 0.00013 562 1.96199 0.00013 5631.96183 0.00013 564 1.96168 0.00013 565 1.96152 0.00013 566 1.961370.00012 567 1.96122 0.00012 568 1.96106 0.00012 569 1.96091 0.00012 5701.96076 0.00012 571 1.96061 0.00012 572 1.96046 0.00012 573 1.960320.00012 574 1.96017 0.00012 575 1.96002 0.00012 576 1.95988 0.00012 5771.95973 0.00011 578 1.95959 0.00011 579 1.95945 0.00011 580 1.959310.00011 581 1.95917 0.00011 582 1.95903 0.00011 583 1.95889 0.00011 5841.95875 0.00011 585 1.95861 0.00011 586 1.95847 0.00011 587 1.958340.00011 588 1.9582 0.00011 589 1.95807 0.0001 590 1.95793 0.0001 5911.9578 0.0001 592 1.95766 0.0001 593 1.95753 0.0001 594 1.9574 0.0001595 1.95727 0.0001 596 1.95714 0.0001 597 1.95701 0.0001 598 1.956880.0001 599 1.95676 0.0001 600 1.95663 0.0001 601 1.9565 0.0001 6021.95638 0.00009 603 1.95625 0.00009 604 1.95613 0.00009 605 1.9560.00009 606 1.95588 0.00009 607 1.95576 0.00009 608 1.95564 0.00009 6091.95552 0.00009 610 1.9554 0.00009 611 1.95528 0.00009 612 1.955160.00009 613 1.95504 0.00009 614 1.95492 0.00009 615 1.9548 0.00009 6161.95469 0.00009 617 1.95457 0.00008 618 1.95446 0.00008 619 1.954340.00008 620 1.95423 0.00008 621 1.95411 0.00008 622 1.954 0.00008 6231.95389 0.00008 624 1.95378 0.00008 625 1.95366 0.00008 626 1.953550.00008 627 1.95344 0.00008 628 1.95333 0.00008 629 1.95322 0.00008 6301.95312 0.00008 631 1.95301 0.00008 632 1.9529 0.00008 633 1.952790.00007 634 1.95269 0.00007 635 1.95258 0.00007 636 1.95248 0.00007 6371.95237 0.00007 638 1.95227 0.00007 639 1.95216 0.00007 640 1.952060.00007 641 1.95196 0.00007 642 1.95186 0.00007 643 1.95176 0.00007 6441.95165 0.00007 645 1.95155 0.00007 646 1.95145 0.00007 647 1.951350.00007 648 1.95125 0.00007 649 1.95116 0.00007 650 1.95106 0.00007 6511.95096 0.00007 652 1.95086 0.00006 653 1.95077 0.00006 654 1.950670.00006 655 1.95058 0.00006 656 1.95048 0.00006 657 1.95039 0.00006 6581.95029 0.00006 659 1.9502 0.00006 660 1.9501 0.00006 661 1.950010.00006 662 1.94992 0.00006 663 1.94983 0.00006 664 1.94973 0.00006 6651.94964 0.00006 666 1.94955 0.00006 667 1.94946 0.00006 668 1.949370.00006 669 1.94928 0.00006 670 1.94919 0.00006 671 1.94911 0.00006 6721.94902 0.00006 673 1.94893 0.00006 674 1.94884 0.00005 675 1.948760.00005 676 1.94867 0.00005 677 1.94858 0.00005 678 1.9485 0.00005 6791.94841 0.00005 680 1.94833 0.00005 681 1.94824 0.00005 682 1.948160.00005 683 1.94808 0.00005 684 1.94799 0.00005 685 1.94791 0.00005 6861.94783 0.00005 687 1.94774 0.00005 688 1.94766 0.00005 689 1.947580.00005 690 1.9475 0.00005 691 1.94742 0.00005 692 1.94734 0.00005 6931.94726 0.00005 694 1.94718 0.00005 695 1.9471 0.00005 696 1.947020.00005 697 1.94694 0.00005 698 1.94687 0.00005 699 1.94679 0.00005 7001.94671 0.00005 701 1.94663 0.00004 702 1.94656 0.00004 703 1.946480.00004 704 1.94641 0.00004 705 1.94633 0.00004 706 1.94625 0.00004 7071.94618 0.00004 708 1.94611 0.00004 709 1.94603 0.00004 710 1.945960.00004 711 1.94588 0.00004 712 1.94581 0.00004 713 1.94574 0.00004 7141.94566 0.00004 715 1.94559 0.00004 716 1.94552 0.00004 717 1.945450.00004 718 1.94538 0.00004 719 1.94531 0.00004 720 1.94524 0.00004 7211.94517 0.00004 722 1.9451 0.00004 723 1.94503 0.00004 724 1.944960.00004 725 1.94489 0.00004 726 1.94482 0.00004 727 1.94475 0.00004 7281.94468 0.00004 729 1.94461 0.00004 730 1.94455 0.00004 731 1.944480.00004 732 1.94441 0.00004 733 1.94434 0.00004 734 1.94428 0.00003 7351.94421 0.00003 736 1.94415 0.00003 737 1.94408 0.00003 738 1.944010.00003 739 1.94395 0.00003 740 1.94388 0.00003 741 1.94382 0.00003 7421.94376 0.00003 743 1.94369 0.00003 744 1.94363 0.00003 745 1.943560.00003 746 1.9435 0.00003 747 1.94344 0.00003 748 1.94338 0.00003 7491.94331 0.00003 750 1.94325 0.00003 751 1.94319 0.00003 752 1.943130.00003 753 1.94307 0.00003 754 1.94301 0.00003 755 1.94294 0.00003 7561.94288 0.00003 757 1.94282 0.00003 758 1.94276 0.00003 759 1.94270.00003 760 1.94264 0.00003 761 1.94259 0.00003 762 1.94253 0.00003 7631.94247 0.00003 764 1.94241 0.00003 765 1.94235 0.00003 766 1.942290.00003 767 1.94223 0.00003 768 1.94218 0.00003 769 1.94212 0.00003 7701.94206 0.00003 771 1.94201 0.00003 772 1.94195 0.00003 773 1.941890.00003 774 1.94184 0.00003 775 1.94178 0.00003 776 1.94172 0.00003 7771.94167 0.00003 778 1.94161 0.00002 779 1.94156 0.00002 780 1.94150.00002 781 1.94145 0.00002 782 1.94139 0.00002 783 1.94134 0.00002 7841.94129 0.00002 785 1.94123 0.00002 786 1.94118 0.00002 787 1.941130.00002 788 1.94107 0.00002 789 1.94102 0.00002 790 1.94097 0.00002 7911.94091 0.00002 792 1.94086 0.00002 793 1.94081 0.00002 794 1.940760.00002 795 1.94071 0.00002 796 1.94066 0.00002 797 1.9406 0.00002 7981.94055 0.00002

Modeled Example 11 is an article having a structure as shown in Table 16and includes a chemically strengthened ABS glass substrate and ananti-reflection coating disposed on the substrate. The anti-reflectioncoating materials and thicknesses of each layer of material, in theorder arranged in the anti-reflection coating, are provided in Table 16.

TABLE 16 Structure of Modeled Example 11, in pristine condition.Material Thickness (nm) Air Immersed SiO₂ 95 AlO_(x)N_(y) 167  SiO₂ 31AlO_(x)N_(y) 37 SiO₂ 57 AlO_(x)N_(y) 14 ABS glass immersed

FIG. 14A illustrates the change in modeled reflectance of the coatedsurface of Modeled Example 11 in pristine condition, at differentincident illumination angles. FIG. 14B illustrates the a* and b* colorcoordinates in reflection of the coated surface under a 10 degreeobserver and under a D65 illuminant and F2 illuminant.

Modeled Example 12 is an article having a structure as shown in Table 17and includes a chemically strengthened ABS glass substrate and ananti-reflection coating disposed on the substrate. The anti-reflectioncoating materials and thicknesses of each layer of material, in theorder arranged in the anti-reflection coating, are provided in Table 17.

TABLE 17 Structure of Modeled Example 12, in pristine condition.Thickness Refractive Extinction Optical Thickness Material (nm) IndexCoefficient (FWOT) Air Immersed 1 0 SiO₂ 107 1.4764 0.00005 0.2867163AlO_(x)N_(y) 44 1.98107 0 0.15888173 SiO₂ 10 1.4764 0.00005 0.02754151AlO_(x)N_(y) 86 1.98107 0 0.31124395 SiO₂ 26 1.4764 0.00005 0.06990069AlO_(x)N_(y) 27 1.98107 0 0.09595578 SiO₂ 47 1.4764 0.00005 0.12707752AlO_(x)N_(y) 9 1.98107 0 0.03083264 ABS glass Immersed 1.51005 0

FIG. 15A illustrates the change in modeled reflectance of the coatedsurface of Modeled Example 12 in pristine condition, at differentincident illumination angles. FIG. 15B illustrates a* and b* colorcoordinates in reflection of the coated surface under a 10 degreeobserver and under a D65 illuminant and F2 illuminant.

As shown in the Examples, where surface defects including surfacethickness removal are evaluated, as the surface thickness increased from0 nm up to about 150 nm, the reflectance tends to increase and thereflected color also changes continuously or quasi-continuously, asshown in Figures. No discontinuous jumps in the reflectance, contrastratios, or color shifts were observed at any surface thickness removal.

Without being bound by theory, it is believed that the lower absolutereflectance of some anti-reflection coatings according to one or moreembodiments having a surface defect of the addition of a fingerprintdroplet (when compared to higher reflectance observed in a conventionalanti-reflection coatings with the same fingerprint residue) may beexplained by a lower reflectance at the interface between thefingerprint droplet and anti-reflection coating according to one or moreembodiments as compared to the interface between the fingerprint residueand conventional anti-reflection coating, as shown in FIGS. 11A-B, 12A-Band 13A-B. Stated another way, because the conventional anti-reflectioncoating is more perfectly impedance-matched to air, it is less perfectlyimpedance-matched to fingerprint oils. While the anti-reflectioncoatings according to one or more embodiments may be less perfectlyimpedance-matched to air, they can be more perfectly impedance-matchedto fingerprint oils, resulting in a lower total reflectance, as comparedto a conventional anti-reflection coatings, when both are combined witha surface defect including a fingerprint droplet having a finitethickness (e.g., from about 100 nm to about 2000 nm) disposed on thecoated surface and surrounded by air.

Without being bound by theory, some embodiments of the anti-reflectioncoatings described herein may exhibit a higher reflectance at somevisible wavelengths; however at the system level (i.e., when combinedwith other elements of a display or electronic device), this increase inreflectance can be less significant than it appears at the componentlevel (i.e., in the article without the other elements of a display orelectronic device). Specifically, buried surface reflections in therange from about 0.5% to about 3% are common in displays, even thosethat have a directly adhesive-bonded cover material. A display devicehaving buried surface reflections of about 2% will have a totalreflectance of about 2.1% when combined with a conventionalanti-reflection coating having reflectance of 0.1%. Accordingly, thesame display device will have a total reflectance of 3.2% when combinedwith an anti-reflection coating according to one or more embodimentshaving reflectance of 1.2%. This difference is relatively small, andboth coatings impart substantially lower reflectance than the samedisplay system would have without any anti-reflection coating (i.e.,uncoated glass exhibits about 6% reflectance and uncoated sapphireexhibits about 10% reflectance).

The anti-reflection coating designs described herein can be adjusted toaccommodate surface defects of different sizes or having refractiveindices. For example, the thicknesses of the layers can be adjustedwithout departing from the spirit of the invention. In one example, theanti-reflection coating could include a scratch resistant layer that is2000 nm thick; however this layer may be made thinner (e.g., in therange from about 100 nm to about 2000 nm), while still providing someresistance to scratch, abrasion, or damage events, potentially includingdrop events such as when an article is dropped onto a hard surface suchas asphalt, cement, or sandpaper. In other examples, the scratchresistant layer can be made thicker (e.g., in the range from about 2000nm to about 10000 nm thick). The top layer of the anti-reflectioncoating (which includes SiO₂ in the examples) can have varyingthicknesses. In one embodiment, the thickness is in the range from about1 nm to about 200 nm. A top SiO₂ layer can also provide compatibilitywith additional coatings disposed on the anti-reflection coating such assilane-based low-friction coating layers, including fluorosilane layers,alkyl silane layers, silsesquioxane layers, and the like, that may beformed by liquid deposition or vapor deposition means.

It will be apparent to those skilled in the art that variousmodifications and variations can be made without departing from thespirit or scope of the invention.

What is claimed is:
 1. An article, comprising: a substrate having asubstrate surface; and an anti-reflection coating disposed on thesubstrate surface forming a coated surface, wherein the anti-reflectioncoating comprises a first low RI sub-layer and a second high RIsub-layer, wherein the first low RI sub-layer comprises SiO₂, Al₂O₃,GeO₂, SiO, AlO_(x)N_(y), SiO_(x)N_(y), Si_(u)Al_(v)O_(x)N_(y), MgO,MgF₂, BaF₂, CaF₂, DyF₃, YbF₃, YF₃, CeF₃, or combinations thereof,wherein the second high RI sub-layer comprises Si_(u)Al_(v)O_(x)N_(y),AlN, AlO_(x)N_(y), SiO_(x)N_(y), HfO₂, Y₂O₃, MoO₃, or combinationsthereof, and further wherein the coated surface exhibits a first averagereflectance when the coated surface is in a pristine condition, and asecond average reflectance after removal of a surface thickness of about20 nm to about 500 nm of the anti-reflection coating from the coatedsurface that provides a contrast ratio (the second average reflectance:the first average reflectance) in the range from about 0.5 to about 50,over the visible spectrum, wherein the anti-reflection coating has athickness that is greater than the surface thickness and wherein thereflectance is measured under a CIE illuminant.
 2. The article of claim1, wherein the second high RI sub-layer is disposed over the substratesurface and the first low RI sub-layer is disposed over the second highRI sub-layer.
 3. The article of claim 1, wherein the first low RI layercomprises SiO₂ and the second RI layer comprises Si_(u)Al_(v)O_(x)N_(y),SiO_(x)N_(y), AlO_(x)N_(y), or combinations thereof.
 4. The article ofclaim 1, wherein the anti-reflection coating comprises a plurality ofsub-layer sets, each sub-layer set comprising the first low RI sub-layerand the second high RI sub-layer.
 5. The article of claim 1, wherein thecontrast ratio is from about 0.5 to about
 10. 6. The article of claim 1,wherein the anti-reflection coating further comprises ascratch-resistant coating, the scratch-resistant coating comprisingSi_(u)Al_(v)O_(x)N_(y), Ta₂O₅, Nb₂O₅, AlN, Si₃N₄, AlO_(x)N_(y),SiO_(x)N_(y), HfO₂, TiO₂, ZrO₂, Y₂O₃, Al₂O₃, MoO₃, or combinationsthereof.
 7. The article of claim 6, wherein the scratch-resistantcoating further comprises a hardness of about 5 GPa or greater and athickness from about 100 nm to about 10000 nm.
 8. The article of claim6, wherein the scratch-resistant coating further comprises a hardness ofabout 5 GPa or greater and a thickness from about 1000 nm to about 10000nm.
 9. An article, comprising: a substrate having a substrate surface;and an anti-reflection coating disposed on the substrate surface forminga coated surface, wherein the anti-reflection coating comprises a firstlow RI sub-layer, a second high RI sub-layer, and a scratch-resistantlayer, wherein the first low RI sub-layer comprises an oxide, anoxynitride, a fluoride, or combinations thereof, wherein the second highRI sub-layer comprises an oxide, an oxynitride, a nitride, orcombinations thereof, wherein the scratch-resistant layer comprisesSi_(u)Al_(v)O_(x)N_(y), Si₃N₄, AlO_(x)N_(y), SiO_(x)N_(y), orcombinations thereof, wherein the scratch-resistant coating furthercomprises a hardness of about 5 GPa or greater and a thickness fromabout 100 nm to about 10000 nm, and further wherein the coated surfaceexhibits a first average reflectance when the coated surface is in apristine condition, and a second average reflectance after removal of asurface thickness of about 20 nm to about 500 nm of the anti-reflectioncoating from the coated surface that provides a contrast ratio (thesecond average reflectance: the first average reflectance) in the rangefrom about 0.5 to about 50, over the visible spectrum, wherein theanti-reflection coating has a thickness that is greater than the surfacethickness and wherein the reflectance is measured under a CIEilluminant.
 10. The article of claim 9, wherein the second high RIsub-layer is disposed over the substrate surface and the first low RIsub-layer is disposed over the second high RI sub-layer.
 11. The articleof claim 9, wherein the first low RI layer comprises SiO₂ and the secondRI layer comprises SiO_(x)N_(y), Si₃N₄ or combinations thereof.
 12. Thearticle of claim 9, wherein the anti-reflection coating comprises aplurality of sub-layer sets, each sub-layer set comprising the first lowRI sub-layer and the second high RI sub-layer.
 13. The article of claim9, wherein the contrast ratio is from about 0.5 to about
 10. 14. Thearticle of claim 13, wherein the scratch-resistant coating furthercomprises a thickness from about 1000 nm to about 10000 nm.
 15. Anarticle comprising: a substrate having a substrate surface; and ananti-reflection coating disposed on the substrate surface forming acoated surface, wherein the anti-reflection coating comprises a firstlow RI sub-layer and a second high RI sub-layer, wherein the first lowRI sub-layer comprises SiO₂, Al₂O₃, GeO₂, SiO, AlO_(x)N_(y),SiO_(x)N_(y), Si_(u)Al_(v)O_(x)N_(y), MgO, MgF₂, BaF₂, CaF₂, DyF₃, YbF₃,YF₃, CeF₃, or combinations thereof, wherein the second high RI sub-layercomprises Si_(u)Al_(v)O_(x)N_(y), AlN, AlO_(x)N_(y), SiO_(x)N_(y), HfO₂,Y₂O₃, MoO₃, or combinations thereof, and further wherein the coatedsurface of the article exhibits a first average reflectance in the rangefrom about 0.6% to about 6.0% over a visible spectrum in the range fromabout 450 to about 650 nm as tested when the article is in a pristinecondition, and a second average reflectance of about 10% or less overthe visible spectrum as tested when the coated surface comprises a layerof fingerprint-simulating medium having a thickness in the range fromabout 100 nm to about 2000 nm, wherein the fingerprint-simulating mediumcomprises a refractive index of 1.4-1.6.
 16. The article of claim 15,wherein the second high RI sub-layer is disposed over the substratesurface and the first low RI sub-layer is disposed over the second highRI sub-layer.
 17. The article of claim 15, wherein the first low RIlayer comprises SiO₂ and the second RI layer comprisesSi_(u)Al_(v)O_(x)N_(y), SiO_(x)N_(y), AlO_(x)N_(y), or combinationsthereof.
 18. The article of claim 15, wherein the anti-reflectioncoating comprises a plurality of sub-layer sets, each sub-layer setcomprising the first low RI sub-layer and the second high RI sub-layer.19. The article of claim 15, wherein the anti-reflection coating furthercomprises a scratch-resistant coating, the scratch-resistant coatingcomprising Si_(u)Al_(v)O_(x)N_(y), Ta₂O₅, Nb₂O₅, AlN, Si₃N₄,AlO_(x)N_(y), SiO_(x)N_(y), HfO₂, TiO₂, ZrO₂, Y₂O₃, Al₂O₃, MoO₃, orcombinations thereof.
 20. The article of claim 19, wherein thescratch-resistant coating further comprises a hardness of about 5 GPa orgreater and a thickness from about 100 nm to about 10000 nm.